Skip to main content

A registered result in its source context

Original ledger classification: Clockwork coherence [E]/[C] (Coxeter primes = anchor atoms = facet fields; chi=3^6/(3^6-2^6); both dynamic rates carry prime-2; 30=5x6) -- a bird's-eye re-reading, no new number

Recorded statement: The clockwork coherence (2026-06-24, bird's-eye): the three Coxeter primes ARE the three anchor atoms ARE the three number-field facets, and the prime-2 seam is the common dynamical factor. A re-reading tying v390 (facets) to the anchor…

Statement, assumptions and sources

Paper context: Origin Theory

The exact identifier, original classification and full claim are available below.

The source wording and classification below are preserved as recorded. A paper link, shared script or authored topic relation does not upgrade the claim or report a new proof run. Read later reviewed findings separately.

Read the exact registered claim and its dependencies

COXETER.ATOMS.01

Original ledger classification: Clockwork coherence [E]/[C] (Coxeter primes = anchor atoms = facet fields; chi=3^6/(3^6-2^6); both dynamic rates carry prime-2; 30=5x6) -- a bird's-eye re-reading, no new number

Original claim text

The clockwork coherence (2026-06-24, bird's-eye): the three Coxeter primes ARE the three anchor atoms ARE the three number-field facets, and the prime-2 seam is the common dynamical factor. A re-reading tying v390 (facets) to the anchor a=(1,1,2) and v319 (5x6 clock). [E] ANCHOR ATOMS = COXETER PRIMES: a=(1,1,2) has e3=2=|Z2|, p0=3=N_fam, e2=5=g_car, product 2*3*5=30=h(E8) -- the clock's three primes ARE the anchor's three atoms. [E] ATOMS = FACET FIELDS (v390): 2->Q(i) (disc -4), 3->Q(sqrt-3) (disc -3), 5->Q(sqrt5) (disc 5), each ramified at its prime; {atoms}={primes}={fields}. [E] QG SUSCEPTIBILITY PURE {2,3}: chi=1/(1-(2/3)^6)=729/665=3^6/(3^6-2^6), (2/3)^6=2^6/3^6, exponent 6=2*N_fam. [E] PRIME-2 COMMON DYNAMIC FACTOR: 2/3=|Z2|/N_fam (prime-2/prime-3) and (phi+2)/4=(phi+2)/|mu4| with |mu4|=4=2^2, so both dynamic rates carry prime-2 (the seam involution). [E] 30=5x6=g_car*(2 N_fam) (v319). [C] the prime-2 seam is the universal dynamical engine; prime-3 (family) and prime-5 (carrier golden) the two attractors.

Original classification detail

[E] the exact arithmetic (atoms=primes=fields; chi=3^6/(3^6-2^6); 2/3=|Z2|/N_fam; 4=|mu4|=2^2; 30=5x6); [C] the seam-as-universal-dynamic-engine reading. A re-reading of established atoms/eigenvalues (v390/v319), introduces no new number.

Dependencies as recorded

v314; v319; v383; v387; v390; v23; v53

Open the original ledger source, row 461

Location recorded in the ledger

These document locations are recorded directly on the ledger row. They are document level navigation, rather than a newly inferred section citation.

Sections that explicitly cite this claim

A literal claim identifier is present in these paper sections. The section and its premises determine what the citation supports.

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.

All 9 linked sections

Registered verification modules

  • v394_coxeter_atoms.pyRegistered verification module · frontier
    Read the description recorded in the module registry

    COXETER.ATOMS.01: the clockwork coherence -- the three Coxeter primes ARE the three anchor atoms ARE the three number-field facets, and the prime-2 seam is the common dynamical factor. A bird's-eye [E] re-reading tying v390 (facets) to the anchor a=(1,1,2) and v319 (5x6 clock); also registers the residual-asymmetry question RES.COXETER.SYMMETRY.01 as a tracked [O]. [E] a=(1,1,2): e3=2=|Z2|, p0=3=N_fam, e2=5=g_car, product 30=h(E8). [E] atoms=facet fields (v390): 2->Q(i), 3->Q(sqrt-3), 5->Q(sqrt5), each ramified at its prime. [E] chi=729/665=3^6/(3^6-2^6), (2/3)^6=2^6/3^6, exponent 6=2 N_fam. [E] both dynamic rates carry prime-2: 2/3=|Z2|/N_fam, (phi+2)/4=(phi+2)/|mu4|, |mu4|=4=2^2. [E] 30=5x6=g_car*(2 N_fam). [C] the seam is the universal dynamic engine. [O] RES.COXETER.SYMMETRY.01 registered, not closed.

A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.

Search later reviewed research for this identifierRead the coverage boundaries