Exact representation-theoretic certificate for the icosahedral closure theorem: the twelve-port screen module, the compact-Lie trichotomy, the rank-five noncentral corollary, and the oriented face-phase multiplicities.
Referenced as the
closure certificate in paper/observers_are_all_you_need.tex and
paper/recovering_relativity_..._compact.tex.
python3 a5_screen_sm_closure.py # module identity, trichotomy, face phases, kinetic relation
python3 exterior_sm_completion.py # exterior matter, anomalies, weak load, deck control
python3 a5_selection_certificate.py # sharpness data for Cohn-Kumar universal optimality
python3 echosahedral_selector_certificate.py all # issue #565 source selector, receipt, controls
python3 port_current_inner_certificate.py all # issue #566 physical port-current algebra, receipt, controls
python3 super_tannakian_matter_lift_certificate.py all # issue #314 super-Tannakian matter lift, receipt, controls
python3 axis_center_descent_certificate.py all # issue #567 conditional kernel/lattice receipt and physical no-go
python3 coset_carrier_certificate.py all # A1 carrier as coset geometry of a supplied SL(2,5) source, 900 placements, receipt, controls
python3 sl2f5_port_spin_bridge_certificate.py verify # exact SL(2,F5) to PORT-SPIN-LIFT bridge
python3 sl2f5_mckay_e8_certificate.py verify # exact McKay graph of the certified spin doublet: affine E8, Galois control
python3 verify_galois_port_frame_independent.py # incidence-derived two-frame geometry and exact degrees 1/7
python3 galois_source_response_control.py # bounded non-selection under complete source-law conjugation
python3 source_repair_generator_certificate.py # exact seam-law classification and source-receipt boundary
python3 native_defect_stability_gate.py # native flatness versus declared puncture/flux protection
python3 verify_source_repair_generator_independent.py # independent incidence, invariant-weight and receipt checks
python3 source_current_tomography_stage0.py verify # source-current tomography Stage 0 baseline pins
python3 source_current_tomography_stage1_contract.py verify # Stage 1 admissibility contract
python3 source_current_order_sensitive_inventory.py all # Stage 2 bounded inventory and certificate
python3 verify_source_current_order_sensitive_inventory.py --inventory manifests/source_current_order_sensitive_inventory.json # independent Stage 2 verifier
python3 -m unittest discover -s tests -v # issue #565/#566/#314/#567 regression and adversarial suites
python3 a5_compact_lie_classifier.py # compact-Lie enumeration
python3 a5_harmonic_decomposition.py # angular multiplet sequence
python3 bh_log_correction.py # conditional horizon log-coefficient decision tree
python3 independent_trichotomy_check.py # independent re-derivation, trusts nothing above
python3 claim_boundary_certificates.py # exact Q0 fixtures and physical-boundary controls
python3 digest_conventions.py # classify every path-paired pin by the serialization that reproduces it
python3 test_audit.py # regression suiteRequires Python 3.11+ and SymPy. The independent cross-check
independent_lane_check.py also needs NumPy. The suite exits 0.
The source-repair checks consume the observer-like patch's local port
incidence, record-conserving repair relation and scheduler/readback receipts.
They distinguish an invariant linear seam generator from the full nonlinear
integer repair process; their conditional band result does not select a
physical proposal law. Run their mutation controls with
python3 -m unittest discover -s tests -p test_source_repair_generator_certificate.py.
The Galois frame attachment certificate
constructs both rank-three Gram frames directly from the committed oriented
incidence. The marked order-five traces, Laplacian modes, chord rankings and
oriented degrees distinguish the two frames exactly. The audited A1 support
bridge has no source-bound identification with these local radial face maps;
PORT-GRAM-SUPPORT-ATTACHMENT is absent. The integrated source-response
clauses pass for both fully conjugate laws. The verdict is
GALOIS_FRAME_AMBIGUITY_PERSISTS_WITHOUT_SUPPORT_ATTACHMENT, with no physical
selection or numerical prediction. Its two-frame menu is separate from the
orientation-preserving/full-automorphism menu in the selection ledger.
Two scripts in this directory corroborate in floating point and carry none
of this exactness. a5_harmonic_decomposition.py evaluates characters with
math.sin and accepts a multiplicity within 1e-8 of an integer; its exact
counterpart is the Lean receipt Lean/Screen/A5AngularMultiplets.lean.
independent_lane_check.py decides ranks with a 1e-8 tolerance and
cross-checks the exact Lean modules it names (A5Commutant, A5SixAxes,
TraceBalancedKernel, TrichotomyCases, UnitSplit12).
| Object | Statement |
|---|---|
| Echosahedral counting and incidence selector (#565, #625, #628) | On the declared federation-of-twelve-port-echosahedra branch, twelve primitive central atoms of trace 1/12, an additional integer atom-counting grammar on the total-12 fiber, and the normalized central-readback Hilbert-Schmidt cost give the unique all-one split with exact quadratic gap 2. The complete #625 diagram classification fixes additive counting up to one positive unit scale, so the half-unit readback is a units rescaling rather than a half-event implementation. The #628 patch machine generates integer event counts, applies register-level conservative repairs, and derives its move-count settling cost from those dynamics. Every move lowers the load-square Lyapunov function by the exact amount 2(d-1); the seam quadratic and the A3 Hessian remain separate comparison objects. Oriented edge/face incidence and the refinement lineage independently give the unique graph-distance-three antipode, Aut+ = A5 by a faithful conjugation action on five Klein-four subgroups, six axes, and the exact rank-three Gram frame G^2=4G. |
| A1/A2 Lie-type theorem and conditional current witness (#566, #599) | The twelve-port module is 1+3+3'+5. A faithful compact commutator-closed response tangent with endogenous proper-A5 holonomy has centre dimension at most one; its one fixed line excludes the centreless su(2)^4 branch, so compact classification forces u(1)+su(2)+su(3). The source artifact independently derives R=-J, its four sector signs, the oriented frame, and carrier persistence. It does not select a matrix current or reconstruct a bracket. The declared charged-double-triplet fixture realizes the forced Lie type exactly as u(3)+so(3). Its physical source gate is false until ordered current tomography and same-current overlap holonomy are produced. Twenty-four negative controls fail closed. Lean bridge: Lean/Screen/A2HolonomyBridge.lean; executable theorem and fixture: port_current_inner_certificate.py. |
| Source-current tomography Stage 2 bounded inventory (#734) | A pinned audit of 33 source, runtime, algebraic, refinement, formal, and physical-current packets finds zero objects that jointly provide twelve reversible source-native W12 perturbation families, both mixed composition orders as raw histories, target freedom, and refinement provenance. The icosahedral adjacency-response candidate is four-dimensional and commutative; the logged W12/refinement packet is irreversible and order-erasing; the full-family routed read compiler retains regenerated q=13/q=21 histories with refinement provenance but executes resets and destructive means in every hop and proves its readouts schedule-independent. Facts from those distinct packets are not composited. A canonical content snapshot records the path, byte count, and SHA-256 digest of all 851 included files below the 35 audited directories, including the runtime packages, production receipts, and physical-current packages that join the scope at the audited baseline, so path and byte drift fail closed. The verdict SOURCE_CURRENT_ORDER_SENSITIVE_OBJECT_NOT_PRESENT applies only to the enumerated reviewed source scope and authorizes no positive tomography stage or physical-current claim. Producer, independent verifier, mutation gates, and detailed boundary: source_current_order_sensitive_inventory.py, verify_source_current_order_sensitive_inventory.py, and source_current_tomography_stage2.md. |
| Conditional super-Tannakian matter lift (#314) | Given the declared charged-double-triplet current fixture, the finite packet checks the non-split binary-icosahedral lift, the faithful action on V=C (+) W, the rank-15 exterior projector Lambda^2 V + Lambda^4 V, the Standard Model hypercharge multiset, chirality, anomaly traces, Witten parity, three invariant Yukawa lines, and the common central kernel. The exhaustive 1024-subset scan leaves the unordered conjugate rank-15 pair as the unique nonempty chiral anomaly-free selection inside the declared exterior menu. The finite Spin artifact fixes odd-Weyl typing inside this construction. It does not source-select the current representation, the physical matter action, one conjugate representative, a scalar sector, or a continuum Spin attachment. The conditional algebraic gate passes and the physical matter-source gate fails closed. Twenty typed controls pass. |
| Conditional axis-centre descent (#567) | On the declared matter table, exhaustive central enumeration gives the diagonal common kernel generated by (omega_3 I_3, -I_2, e^{i pi/3}) and the maximal effective image (SU(3) x SU(2) x U(1))/Z6. Local tensors also descend through the cover and the Z2 and Z3 quotients, so they do not select a global form. The six-axis calculation has Smith residue six only after diagonal and zero-sum coefficient relations are declared. The exact generator intertwiner and line-polarization calculations are conditional on that relation system. A complete source character category, a same-source loop-to-kernel theorem, source-selected matter, and laboratory attachment remain open. The physical global-form gate fails closed. Lean: Z6Descent.lean, ExteriorSelection.lean; executable receipt schema v4. |
| Coset carrier from a supplied binary icosahedral source (discussion #769) | Taking SL(2, F_5) as the supplied source, the coset geometry of its central quotient G (vertices G/C5, faces G/C3, edges G/C2, incidence by nonempty coset intersection) is classified for all 900 placements of the three cyclic subgroups. All 900 have the same local incidence counts. Exactly 120, the placements admitting generators with xyz = 1, close into a coherently oriented triangulated surface and relabel onto the committed PortFrameGram adjacency, CoreAxioms.orientedFaces, and the sixty A5PortAction rows; they form one orbit under the exhaustively enumerated Aut(G). A further 180 share the committed edge graph and face vertex sets and fail the coset edge-face incidence. The result is conditional on the supplied group. Receipt, fifteen typed controls, and tests: coset_carrier_certificate.py; theorem note: coset_carrier_certificate.md. |
Explicit SL(2,F5) / PORT-SPIN-LIFT bridge |
Starting from the supplied SL(2,F5) source and the independently reconstructed conditional PORT-SPIN-LIFT, the bridge derives an orientation-preserving carrier relabelling, matches a presentation triple satisfying a^2 = b^3 = c^5 = abc = -I, exhausts the eight lift-sign choices, extends the selected generator map to all 120 elements, verifies all 14,400 products and all 120 quotient-square identities, and fixes +I -> +I2 and -I -> -I2. The companion Lean module SL2F5PortCover.lean formalizes the canonical surjective SL2F5 -> PortGroup map with kernel equal to the scalar center. This does not invoke McKay/E8, select φ, state a mass relation, or source-select the current fixture. |
| Exact McKay graph of the certified spin doublet | From the faithful two-dimensional representation supplied by the bridge above, exact characters over Q(sqrt(5), i) recover all nine irreducibles of SL(2,F5) (dimensions 1,2,2,3,3,4,4,5,6, squared sum 120) from the symmetric powers Sym^0..Sym^7 and one tensor product, with no hard-coded character table, on nine conjugacy classes derived from the source. The fusion matrix N_ij = <chi_2 chi_i, chi_j> is a simply-laced tree with A d = 2 d and is isomorphic to affine E8 by a dimension-preserving map; -I splits the irreducibles five center-trivial and four spinorial. The sqrt(5) -> -sqrt(5) conjugate doublet is again faithful and again gives affine E8, so the graph type does not select φ over its conjugate. This does not state a mass relation, identify the finite spin action with physical rotations, source-select the current fixture, or formalize McKay or E8 in Lean. |
| Vertex module | chi_P12 = (12,0,0,2,2), so P12 = 1 + 3 + 3' + 5, multiplicity-free |
| Adjacency spectrum | det(xI-A) = (x-5)(x+1)^5(x^2-5)^3 → canonical ranks 1,3,3,5 |
| SM adjoint restriction | ad su(3) = End_0(3') = 3' + 5; with su(2) → 3, u(1) → 1, the total is 1 + 3 + 3' + 5 |
| Icosahedral selection | 3 distinct inner products {-1, ±1/sqrt5}, spherical 5-design ⇒ sharp (m=3, strength 2m-1=5). By Cohn–Kumar (JAMS 20, 2007) it uniquely minimizes every strictly completely monotonic pair cost of squared distance, up to O(3). |
| D-optimal selector | Maximizing det(F1) det(F2) at fixed vector/quadrupole trace gives F1=2 I3, F2=(4/5) I5; the six centered projectors form a regular simplex, hence the unique real ETF(3,6), the icosahedral axes. This is an independent optimality cross-check. The certified echosahedral-federation branch uses the declared counting/cost and incidence packet instead. |
| Compact-Lie trichotomy | Exactly three algebras: u(1)^12, su(2)^2 + u(1)^6, su(3) + su(2) + u(1) |
| Inner-action closure | If the A5 action is inner: dim Z(g) <= 1 (inner autos fix the center pointwise); Z(g)=0 forces su(2)^4 whose fixed-space dimension is a multiple of 3, contradicting dim g^{A5}=1; hence dim Z(g)=1, semisimple dim 11, and 11=8+3 uniquely ⇒ su(3)+su(2)+u(1). Needs no W5-NONCENTRAL receipt. |
| Angular multiplets | l=2: 5 (irreducible); l=3: 3'+4; l=4: 4+5; l=5: 3+3'+5; l=6: 1+3+4+5. First nonconstant invariant at l=6. Frozen forward target FZ-02 with kill bands and timestamped custody; Lean receipt A5AngularMultiplets.lean; deterministic receipt via a5_harmonic_decomposition.py --receipt. |
| Horizon log coefficient | Conditional decision tree, not a universal law. Unconstrained q-state cells give S=K log q exactly, i.e. c=0. Exact 12-port balance: c=11/2. 24-slot balance: c=23/2. Nonabelian SU(3)xSU(2) singlet saddle: c=11/2. Full 12-dim gauge singlet incl. U(1): c=6. The horizon measure must be derived before c is frozen. |
| Rank-five corollary | W_5 noncentral ⇒ su(3) + su(2) + u(1) uniquely |
| Face-phase multiplicities | m_w = (dim V - chi_V(3A))/3 = (0,1,1,1,2) on (1,3,3',4,5); minimal nontrivial extension has dimension 3 |
| Missing-four/Higgs no-go | Rejected. End_{A5}(4) = R, so no A5-invariant complex structure exists for a commuting hypercharge U(1). The identity 1+3+3+4+5=16 is dimensional only. |
| Exterior matter witness | On a declared trace-balanced carrier V=C+W, the selected non-vacuum even package Lambda^2 V + Lambda^4 V is one 15-state chiral Standard Model generation. Its hypercharges, three one-Higgs invariant lines, perturbative anomalies, and weak-doublet parity check exactly. |
| Weak multiplicity | The exterior package contains three colored weak-doublet copies and one lepton doublet, so the per-generation multiplicity is exactly 4. Its identification with a physical port load requires PORT-LOAD-TRACE. |
| Free-deck control | Any declared free Z6 action on 24 slots has four orbits and a four-dimensional invariant-function space. A physical result requires the deck action and PORT-WEAK-INTERTWINER. |
A compact Lie algebra is reductive, g = z + [g,g], and both summands are
characteristic, hence A5-stable. The identity component of the center is a
torus whose exponential kernel is an integral lattice preserved by every group
automorphism, so the A5-action on z is defined over Q. Because 3 and 3'
are Galois conjugate over Q(sqrt5), a rational submodule contains them with
equal multiplicity. Enumerating rational centers against compact semisimple
dimensions leaves exactly three cases; the other five die because no compact
semisimple algebra has dimension 1, 5, or 7, or because an A1^4 / A1^2
adjoint cannot supply 5 (any homomorphism A5 → S_4 is trivial, A5 being
simple of order 60).
The exact chain is a finite A5 module, a compact coefficient bracket,
trace-balanced block integration under coefficient 1/2, and a six-axis
lattice quotient Z6. Central record projectors commute; the full-rank
compact Lie type follows from the complete faithful A1 response and the A2
same-response internal-holonomy premise. port_current_inner_certificate.py
checks one exact charged-double-triplet matrix witness with four signed
coefficients and an oriented frame. The semantic response artifact derives
the response involution, sector signs, frame, and persistence maps. It does
not reconstruct the matrix generators, their bracket, or same-current
overlap holonomy, so the physical source gate remains false.
super_tannakian_matter_lift_certificate.py verifies the exact non-split
SU(2) double cover, the unordered rank-15 pair selected by the exhaustive
1024-subset anomaly scan, its parity grading, the typing fixed by the
measured centre and section obstruction, the BLOCK-DETERMINANT-BALANCE
charge pair, scalar and channel compatibility, and the emitted action
kernel inside declared current, exterior, and scalar fixtures. Source
selection of the matrix current and physical matter action, scalar
existence and economy, extra-light-sector completeness, continuum Spin
attachment, and laboratory matter identification remain open.
The #567 descent certificate
(axis_center_descent_certificate.py) computes the common kernel on every
declared tensor and the character/cocharacter arithmetic of its maximal
effective quotient. The six-axis class group, flux-sector menu, line
polarization, and refinement checks are exact inside a declared diagonal
and zero-sum relation system. The carrier does not select those relations
or identify its order-six loop class with the complete current and matter
kernel. The physical global-form gate therefore remains false, alongside
the open four-dimensional and laboratory attachments.
native_defect_stability_gate.py checks the executable observer against this
finite flux construction. The closed twelve-port carrier has Euler
characteristic two, five-cycle vertex links and trivial first homology over
both F2 and F3. Deleting one declared face leaves first homology trivial;
deleting an antipodal pair gives one Z6-valued loop generator. All 78 native
load preparations and 4,680 ideal all-seam coin/current branches give zero
face flux because the measured contrast is a port-potential gradient. A
separately declared Z6 link chain has opposite puncture fluxes and is flat
on the other faces. The same first-homology dimensions persist through one exact
edge-midpoint refinement (42 ports, 120 seams, 80 faces); this does not
transport the coarse link connection or define native repair on child cells.
In a link model allowing single-seam updates across the puncture-boundary
seams, the pair can be moved together and annihilated.
Those link updates are not native repair. Gauge invariance of the conditional
flux certificate does not by itself supply a core-protection law or select a
physical defect. The closed carrier retains a second-homology class; trivial
first homology does not exclude curvature or a nontrivial bundle. A globally
assigned link chain has zero total oriented sphere flux. Native repair has no
bundle transition data that would realize a nontrivial second-homology sector.
claim_boundary_certificates.py records five exact-small controls at this
boundary: completion non-identifiability from the current source reduct, the
ten-Majorana rank-15 projector, the distinction between a composite response
cubic and a fundamental 1PI cubic, complement-complete refinement with a
hidden-zero-mode counterexample, and a finite exhaustive settlement fixture.
The matching sorry-free logical no-go is
../../Lean/Screen/PhysicalA5ForcingNoGo.lean.
These are diagnostic Q0 certificates. They do not emit a
physical screen current, a Spin/locality lift, three chiral families, a scalar
field, or a refinement-stable quantum theory.
The family result is therefore split explicitly. The finite screen algebra
supplies a canonical rank-three candidate band, and the declared completion
criterion selects the least admissible multiplicity inside the window
3 <= N_g <= 5. A physical N_g = 3 statement additionally requires the
rank-45 attachment map and the family descent, exchange, residue, and
refinement receipts listed below.
The exterior calculation supplies a second conditional matter route. It does
not turn coefficient directions into physical currents or select the global
form. It is also not the full even Clifford module: that module contains
Lambda^0 V as well as Lambda^2 V + Lambda^4 V. Removing the singlet and
excluding other anomaly-free light sectors requires the explicit source-completeness
premise or a source-derived observer-visible discriminator. Selecting H=W
as the physical scalar is a separate gate. If the face-phase A5 action remains
exact on the family multiplicity space, it restricts Yukawa tensors to
A5-invariant pairings; general family matrices require a source-derived
breaking, hiding, or forgetting mechanism.
- UD12 is exact within the declared realization checked by
echosahedral_selector_certificate.py: the integer total-12 fiber and the normalized central readback normH(q)=sum q_i^2are inputs, andH=12+sum(q_i-1)^2gives the unique all-one minimizer with exact next floor14. - RP-A5 is exact without a downstream representation or measured datum:
the source-oriented incidence produces the unique distance-three antipode,
the positive automorphism group is explicitly
A5, and the distance Gram matrix satisfiesG^2=4G, giving the regular six-axis frame. The theorem, data model, equivalence, refinement proof, and countermodels are incode/a5_closure/echosahedral_selector_certificate.md.
These results use the declared simulator assumption that every local carrier
lineage is a quotient-visible twelve-port echosahedral packet. UD12 also uses
the separately declared integer counting grammar and normalized readback cost.
The complete #625 diagram classification fixes additive counting up to one
positive unit scale. Its half-unit member is the same counting mechanism in a
different unit convention, and the inequivalent 6 I + A comparison is
excluded from the operational cost cone. The #628 mechanism supplies an
operational event-counting and repair-cost realization while retaining the
positive readback scale as a unit convention. The results do not prove that
arbitrary OPH carriers must have this type.
-
The conditional PORT-CURRENT-INNER algebraic construction is verified by
port_current_inner_certificate.py: given the charged-double-triplet model and four signed coefficients, the map is full-rank, compact, closed, A5-equivariant, inner, and natural along the declared algebraic tower maps. These representation data are branch premises, not physical measurements. -
The conditional super-Tannakian matter lift (issue #314) is verified by
super_tannakian_matter_lift_certificate.py: given the pinned conditional #566 packet, the exact non-split SU(2) double cover of the sixty proper implementers (PORT-SPIN-LIFT), the faithful current action on the matter carrier and the fifteen-state module, the derived equivariant projector on the auxiliary CAR/Fock space, realized anomaly and Witten checks, exact chirality and conjugation, three Yukawa invariant lines, naturality along the declared tower and the artifact persistence maps, the emitted action kernel, and the candidate-class nonemptiness witness. The charge pair is derived by BLOCK-DETERMINANT-BALANCE, the scalar and channels by the selection scan, and the category typing is forced by the failing Vec/sVec controls; the kernel emission contract and the candidate-class declaration stay typed declarations. Theorem:code/a5_closure/super_tannakian_matter_lift_certificate.md.
- PORT-CURRENT-INNER verifies the declared charged-double-triplet
fixture. The semantic response artifact determines
R=-J, its relative signs, the oriented frame, and carrier persistence. Ordered source tomography, the bracket, and same-current overlap holonomy are open. - PORT-SPIN-LIFT rides on the conditional current packet. The non-split binary icosahedral cover and its unique involution are exact on the finite Spin fixture. Physical matter and continuum Spin attachment are open.
- BLOCK-DETERMINANT-BALANCE is derived inside the matter packet:
anomaly freedom of the realized package forces the balance line,
primitive integrality and the measured orientation select
(-1/3, 1/2). - AXIS-CENTER-DESCENT computes the common kernel and central descent congruence of the maximal effective image on the declared matter table. The full character lattice also carries the nonabelian highest weights. The six-axis group and polarization use a declared coefficient-relation system. Source completeness and the loop-to-kernel identity are open, as are four-dimensional instanton/theta and laboratory receipts.
- (weaker group-level branch only) A5-COMMON-ACTION + W5-NONCENTRAL:
one group-level action shared by ports and gauge reconstruction, plus one
source-derived repair composition with nonzero projected
W_5commutator. The A1/A2 inner-action theorem above is stronger. - A5-FAMILY-ATTACHMENT (family corollary only): prove the chiral family
fiber's local face-corner phase is the restriction of a global
3or3'action, independent of port labels, worker IDs, chart choices, and refinement presentation. - A5-FAMILY-DESCENT: derive how the selection symmetry is broken, hidden, or forgotten before general family Yukawa matrices are admitted.
- PHYSICAL-GLOBAL-FORM-CONTINUUM (#567 remainder): the deck/loop class, sector menu, polarization, and screen-scope Spin attachment are delivered at finite source scope; the remaining receipts are four-dimensional instanton sectors with topological action normalization (before any theta periodicity statement), monopole dynamics, and laboratory flux measurement (#569 lane).
- EXTERIOR-PACKAGE-SELECTION: the exhaustive 1024-subset anomaly scan
proves the unordered conjugate pair is the unique nonempty chiral
anomaly-free selection at exterior-module scope
(
Lean/Screen/ExteriorSelection.lean). The MGFC-grade exclusion of light sectors beyond the exterior module (direct sums, inert doublets, vectorlike matter, neutral singlets) is owned by #609. - PORT-WEAK-INTERTWINER and PORT-LOAD-TRACE: identify a physical
four-dimensional screen invariant with the four weak-doublet copies and
prove that its normalized additive load is the physical
4Preadout.
If the physical quadratic gauge kinetic operator on the port module is an
adjacency polynomial K = f(A), color coherence (the color triplet and quintet
sharing one kinetic coefficient) forces, at degree two,
k1 = 3*k2 - 2*k3
independent of which inequivalent triplet carries color (both assignments verified). At degree one it collapses to bare coupling unification. A physical discriminator requires a source-derived polynomial degree, kinetic normalization, carrier scale, and complete threshold/RG map. The relation is not a forward test.
Three sha256 serializations produce the pins under manifests/ and
receipts/, and the sha256: string prefix names none of the three.
| Convention | Serialization | Defined in |
|---|---|---|
raw_bytes |
hashlib.sha256(path.read_bytes()): the committed file bytes, trailing newline included |
sha256_file in baryon_dimension_six_census.py |
canonical_json |
hashlib.sha256(json.dumps(value, sort_keys=True, separators=(",", ":"), ensure_ascii=False).encode("utf-8")): compact, key-sorted, no trailing newline |
sha256_json in echosahedral_selector_certificate.py, imported by axis_center_descent_certificate.py and its downstream producers |
canonical_json_self_digest_stripped |
the same compact serialization applied to an artifact body with its own self-digest field deleted | the global_form_artifact self-hash check in axis_center_descent_certificate.py |
The producers write their JSON files with indent=2, sort_keys=True and a
trailing newline, so raw_bytes and canonical_json are two different digests
of one file and neither one can be derived from the other.
One file, receipts/axis_center_descent_reference.receipt.json, is pinned under
two of the three conventions, and the tag distinguishes neither. The digests in
the table below are truncated to their first twelve hex characters.
| Pin site | Value | Convention |
|---|---|---|
receipts/baryon_dimension_six_census.receipt.json, upstream_pins.axis_center_receipt.sha256 |
sha256:c12251507f88… |
raw_bytes |
manifests/common_ew_order_unit_carrier_reference.json, upstream_pins.global_form_receipt.sha256 |
7c854d56af7b… |
canonical_json |
manifests/axis_center_descent_reference.json, global_form_artifact_sha256 |
sha256:0bfdacce8a47… |
canonical_json_self_digest_stripped, over manifests/global_form_semantic_artifact.json |
The field name sha256 therefore covers two conventions, the sha256: prefix
sits on raw-byte and on self-digest-stripped values alike, and the
canonical-JSON pins carry no prefix at all. A reader who picks the wrong
serialization sees a mismatch that reads as a corrupted artifact.
manifests/directed_seam_repair_reference.json states its convention in the
field name itself: its carrier, integer_record_counting_mechanism and
undirected_scheduler pins sit under canonical_json_sha256. That is the
pattern for new pins, because the name travels with the value when a pin is
copied out of its manifest.
The label goes in the pin site and never inside an emitted payload. A payload
field naming its own convention would change the payload bytes and move every
digest taken over them. The axis-centre descent receipt alone is pinned by raw
bytes in receipts/baryon_dimension_six_census.receipt.json and
code/particles/calibration/wz_native_source_packet/outputs/source_parent_inventory.json,
and canonically in manifests/common_ew_order_unit_carrier_reference.json,
manifests/family_band_attachment_reference.json,
manifests/seam_grammar_matter_classification_reference.json and that same
source-parent inventory, with path-level references in
code/particles/runs/status/postdiction_ledger.json,
claims/selection_ledger.json, claims/claim_registry.yaml,
claims/physical_identification_registry.json and docs/POSTDICTION_LEDGER.md.
digest_conventions.py resolves a pin against a file by trying all three
serializations and ignoring both the field name and the tag:
python3 digest_conventions.py # classify every path-paired pin in this package
python3 digest_conventions.py --json # the same classification, per pin
python3 digest_conventions.py \
--digest sha256:c12251507f8843c664854da0682717b3a6b437fdc5632679c7fe1d4918c5d2fb \
receipts/axis_center_descent_reference.receipt.jsonThe sweep walks every path-paired pin under manifests/ and receipts/ and
prints the split:
68 path-paired pins, 0 unreproduced, 0 ambiguous
raw_bytes 8
canonical_json 55
canonical_json_self_digest_stripped 5
A declared pin path that resolves under neither the repository root nor this
directory names a file in an upstream producer checkout; the sweep counts those
sites and leaves them unclassified instead of guessing a third path base, since
a basename collision would otherwise classify the wrong file.
tests/test_digest_conventions.py holds the invariants: every located pin
resolves to exactly one convention, a corrupted pin resolves to none, and the
three conventions give three different digests for one intact file.
Lean/Screen/Compact12.lean formalizes the abstract
u(3) + so(3) matrix commutator, Lie laws, dimension, and a matrix
noncentrality witness. Z6Exact.lean formalizes the six-axis lattice quotient,
S2DesignSignature.lean formalizes the 11/25 arithmetic, and
UnitSplit12.lean proves only that twelve positive integer weights summing to
twelve are all one. A5OPH.lean (merged 2026-07-23 from the external
cross-audit lane, rebuilt under the project toolchain) formalizes the finite
core of the compact-Lie trichotomy (triviality of every A5-action on at
most four objects, the unique partitions 11 = 3+8 and 12 = 3+3+3+3 over
the compact-simple dimension list, the excluded semisimple dimensions
1, 2, 4, 5, 7, the characteristic-centre step) plus the paper's
noncentral-quintet witness, the gluing-class quotient with both invariance
clauses, the A5 ⊄ SU(2) unique-involution obstruction, and the absence of
ℤ/6 in A5. A5CharacterField.lean (#605, closed) proves the
Galois-stability half of the Q(sqrt 5) rationality lemma via the doubled
character table over ℤ[√5], with the torus/cocharacter step a declared
hypothesis. A5SixAxes.lean (#604, closed) lists the sixty elements of the
six-axis PSL(2, F5) action, kernel-checks distinctness, closure,
2-transitivity, and the sharp stabilizer-coset fiber counts, proves the
five-dimensional summand irreducible over ℚ by stabilizer-coset averaging,
and closes the dimension-six branch unconditionally: 1 ⊕ 5 has no
three-dimensional invariant subspace and no 3 + 3 invariant splitting.
A5PortModule.lean (#604, closed) carries the matching S5 centre receipt on
the twelve-port module: the sixty port rotations (row-for-row identical to
A5PortAction.perms) fix exactly the constant line, so a centrally trivial
submodule (the centre under an inner action) has dimension at most
one. A5Commutant.lean (#568, closed) proves the four-orbit structure of
ordered port pairs and the exact four-dimensional orbital commutant of the
port action, with entry invariance equivalent to commutation;
TraceBalancedKernel.lean (#568, closed) checks the six-element cyclic
kernel of the trace-balanced cover on central parameters with bijective
U(1) coordinate; TrichotomyCases.lean (#568, closed) assembles the
centre-versus-semisimple enumeration with every hypothesis in the theorem
signature; UnitSplit12.lean carries removability witnesses for each
unit-splitting premise. The independent cross-check
independent_lane_check.py (this directory) rebuilds the rotation group
from golden-ratio coordinates alone and reproduces the orbit, commutant,
fiber-count, spectrum, kernel, and enumeration data (22 checks, all
passing 2026-07-23). The issue-#565 artifact supplies an exact executable finite
check of the declared integer domain, strict readback cost, antipode, A5
action, frame, refinement, relabelling, and countermodels. The issue-#625
artifact classifies complete additive readbacks as positive multiples of atom
counting and records the exact local A3 expansion: the Kullback-Leibler
second-order Taylor coefficient is 6 I, while the Hessian, equivalently the
Fisher matrix, is 12 I. Neither infinitesimal object supplies the exact
discrete physical cost. The issue-#628 artifact supplies the finite
record-repair mechanism and its derived settling cost. The issue-#566
artifact supplies the exact executable current lift, closure, innerness, and
moduli proofs for the declared charged-double-triplet fixture. The issue-#314 artifact
supplies the exact executable spin lift, matter transport, CAR/Fock
selection, chirality, anomaly, kernel-emission, and declared-tower descent
proofs on top of that packet. A Lean port of those
complete finite packets remains available work; the Python receipts are not
being relabelled as Lean theorems. Phi, Theta, the trace-balanced group,
and physical descent retain their separate support boundaries (the
compact-Lie trichotomy's finite steps are now Lean-checked in A5OPH.lean,
with the former paper steps #604/#605 discharged in A5SixAxes.lean,
A5PortModule.lean, and A5CharacterField.lean, leaving the Lie-theoretic
classical inputs (compact-simple classification, reductive decomposition,
exponential surjectivity, torus/cocharacter step) as the declared
remainder); only the conditional current algebra and the conditional matter
lift are certified here. Source reconstruction of the current and matter
actions remains open.
Finite-group flavor models use triplet representations, and Standard-Model global quotients and line sectors are established subjects. This certificate makes no priority claim. Its scoped result is the full gauge-adjoint module on the icosahedral vertices plus the conditional compact-Lie classification.