Pb-208 and a proposed coherence-capacity bound
Recorded October 25, 2026 · Conjecture, not a derived nuclear stability result. This card curates the operator proposal in ledger 4332. Recording it does not supply a proof, independent nuclear-data validation or physical acceptance.
Proposed scope and arithmetic
The proposal concerns stable nuclei, not a prohibition on heavier radioactive or transient nuclei. It conjectures a single non-self-witnessing reference window containing at most two adjacent four-subcycle construction cycles. If the eight contributions provide independent binary alternatives, their configurations number 256. Four proposed global positional records would leave 252 internal records; a fixed-point-free duality would give 126 two-record orbits.
The numerical bookkeeping is
These identities do not construct any of the required maps. The subcycle labels describe construction/reference structure, not a physical-time bound or a derived nuclear oscillation period. Further construction with retained history and a new reference is not forbidden by the proposed single-window ceiling.
What remains to be constructed
| Proposed bridge | Required source object and test |
|---|---|
| Window bound | A typed witness-dependency/reference structure excluding a ninth independent contribution in the same legitimate window. A source-admitted counterexample would refute that ceiling. |
| Binary capacity | Eight independent binary alternatives on one admitted representation, not eight dependent stages or repeated views of the same data. Enumerate the actual admissible records and test injectivity. There is no supplied 256-record source merely because the arithmetic is available. |
| Positional separation | Explicit extraction and reconstruction maps preserving internal distinctions and the action of changing the barycentre. Four coordinate records are not four independent translations: a barycentric four-tuple has only three independent positional coordinates. |
| Internal duality | An actual fixed-point-free involution on the proposed 252 records, retaining both members of each orbit. Missing duals, fixed points or erased distinctions defeat the pair count. |
| Nuclear interpretation | An independently justified neutron readout and a stability mechanism, plus a proton-sector rule. The accounting does not derive 82 protons or the mass number 208. |
Eight independent binary choices would give 256 configurations, not 256 independent scalar degrees of freedom. Configuration count, record slots, vector-space dimension and information-bit count must not be substituted for one another to justify the subtraction.
Rivals and discriminators
- Longer coherent reference window: exhibit nine independent contributions with explicit noncircular witness dependencies. A third displayed cycle alone is not this test; the question is simultaneous availability under one legitimate reference.
- Dependent choices or a lossy positional split: show that the actual admissible cardinality is different, or that extracting four records loses internal distinctions. Either challenges the stated capacity construction rather than merely its label.
- Non-pairing internal duality: test every proposed record and involution orbit. A fixed point cannot be silently dropped to reach the desired number.
- Routing combinatorics instead of neutron content: the earlier routing audit has equally symmetric counterrules yielding 198 rather than 126 open response pairs. The number 126 in that different model is not independent evidence for this capacity conjecture. Open routing paths and closed loops are not identified localized neutrons.
- Stability needs more than neutron count: the source compares Pb-208 with Bi-209, which also has 126 neutrons but is radioactive. A necessary capacity constraint would not by itself be a complete stability criterion. Do not choose a decay threshold after seeing a candidate.
The existence of heavier unstable nuclei does not refute the stated stable-only scope. A genuinely stable heavier nucleus, or a source-admitted stable construction exceeding the proposed window, would challenge its endpoint claim. The source supplies no binding-energy or lifetime calculation resolving those comparisons.
Evidence and reproduction boundary
The source ledger records the proposal, distinct missing bridges and risky tests. The separate routing-conjecture falsification tests a stronger routing-symmetry claim, not the new reference-window capacity bound. node scripts/falsify-n-routing-conjecture.mjs is not a checker for the capacity conjecture.
The original ledger source and attribution remain unchanged. Neither a new formal proof nor fresh nuclear-data verification is reported here; scientific tests were not rerun for publication. A successful website build only checks publication.
Comparison targets · Results and exclusions · Separate geometric workbench.