A registered result in its source context
Original ledger classification: Reading [E] (marks attractor + tower + cascade) + [C] (Wolfram substrate) + [O] (rewrite-to-full-structure)
Recorded statement: E8 AS A NETWORK ATTRACTOR / WOLFRAM-PROGRAM READING (2026-06-18): an HONEST experimental audit of whether TFPT's structure is naturally a hypergraph/rewrite system, built on the McKay bedrock v219. It does NOT force TFPT into a hypergraph…
Statement, assumptions and sources
Paper context: TFPT — Introduction and reading guide
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Read the exact registered claim and its dependencies
E8.NETWORK.01
Original ledger classification: Reading [E] (marks attractor + tower + cascade) + [C] (Wolfram substrate) + [O] (rewrite-to-full-structure)
Original claim text
E8 AS A NETWORK ATTRACTOR / WOLFRAM-PROGRAM READING (2026-06-18): an HONEST experimental audit of whether TFPT's structure is naturally a hypergraph/rewrite system, built on the McKay bedrock v219. It does NOT force TFPT into a hypergraph nor fabricate a rewrite. [E] E8 MARKS ARE A GRAPH ATTRACTOR: on the affine-E8 / McKay-(2,3,5) 9-node graph (adjacency A, chain n1..n8 + n9 on n6) the minimal lazy local-averaging update m <- (A+2I)/4 m (eigenvalues in [0,1]) converges from ANY positive start to the Kac marks (1,2,3,4,5,6,4,2,3) -- the unique stationary state (A m = 2m, top eigenvalue 2); so the E8 Coxeter skeleton is the unique attractor of a minimal network update. [E] SPHERICAL TOWER TERMINATES AT E8: 2T->E6 (h12), 2O->E7 (h18), 2I->E8 (h30=2*3*5); E8 is the unique top finite-spherical SU(2) case. [E] CASCADE = NESTED-SUBGRAPH COARSE-GRAINING: E8>E7>E6>D5>A4 by node deletion, |roots| 240->126->72->40->20. [C] WOLFRAM-BRIDGE READING: these realise 'E8 is not a fundamental input but the universal attractor of a minimal (2,3,5) network/update' at the Coxeter/network-skeleton level (the user's possibilities 3/4/5) -- an interpretation of verified structure. [O] HONEST SCOPE: the deep question -- a minimal hypergraph REWRITE whose universal attractor is the FULL TFPT structure (E8 LATTICE + recovery dynamics + SM readouts, not just the marks) -- is OPEN. NEG controls: phi0=(4/3)c3=1/(6pi) is the analytic seed, NOT an edge fraction (possibility 4 as literally stated is FALSE); the recovery map is a 1-D Mobius fixed point, not a hypergraph rewrite (possibility 2 is metaphor).
Original classification detail
[E] the E8 marks as the unique attractor of a minimal graph update (on v219's McKay hull), the spherical tower terminus, the cascade coarse-graining; [C] the Wolfram computational-substrate reading; [O] the deep rewrite-to-full-structure question + honest negatives (phi0 is the analytic seed not an edge fraction). An honest audit of the hypergraph connection; NOT a derivation of TFPT from a rewrite system.
Dependencies as recorded
MCKAY.E8.01; COX.TOTATIVE.01; CASCADE.BRIDGE.01
Open the original ledger source, row 398Location recorded in the ledger
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- TFPT — Introduction and reading guide
Navigation through a shared verification script
These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.
- 2026-06-30 (shadow-export coherence — the tfpt5-shadow mirror is now reproducible as shipped: the audit is shadow-aware, the content maps are non-destructive on the website-free subset, and an export gate blocks any incoherent mirror)Research changelog; TFPT — Introduction and reading guide
- The compiler: why [formula in source]TFPT — Introduction and reading guide
- 2026-06-18 (E8 as a network attractor — the Wolfram-program reading, v298)Research changelog; TFPT — Introduction and reading guide
- 2026-06-19 (the hypergraph/Wolfram bridge hardened: the [formula in source] seed reaches [formula in source] as the last finite point, v299)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
Registered verification modules
- v298_e8_network_attractor.pyRegistered verification module · frontier
Read the description recorded in the module registry
E8 as a network attractor — a computational-substrate (Wolfram-program) reading of the (2,3,5)/McKay hull, on the v219 bedrock; an HONEST audit of the 'TFPT as hypergraph' idea, not a derivation. [E] the E8 Kac marks (1,2,3,4,5,6,4,2,3) are the UNIQUE attractor of the minimal lazy graph update m←(A+2I)/4·m on the affine-E8/(2,3,5) McKay graph (converges from any positive start; A·m=2m, top eigenvalue 2). [E] the spherical McKay tower terminates at E8 (2T→E6 h12, 2O→E7 h18, 2I→E8 h30=2·3·5). [E] the E-cascade is nested-subgraph coarse-graining (|roots| 240→126→72→40→20). [C] Wolfram-bridge reading: 'E8 is the universal attractor of a minimal (2,3,5) network' at the Coxeter-skeleton level. [O] the deep question (a minimal hypergraph REWRITE whose attractor is the FULL TFPT structure) stays open; NEG: φ₀=(4/3)c₃=1/(6π) is the analytic seed not an edge fraction, recovery is a 1-D Möbius fixed point not a rewrite.
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