CPT Compact Core FAQ
Assumptions · parameters · open gates · APIs · dual track · what is not claimed
CPT Framework — public integrity note Date: 2026-08-09 Status: ACTIVE · P0.4 · companion to Sol takeaways · A-geom preferred path · spin/FD FAQ §2b · spectrum multiplet card §2d · core v2.15 / \(\mathcal{P}_{\mathrm{EMC}}\) / \(\mathcal{P}_L\) Evidence labels: seeevidence_label_taxonomy.md
Forward plan: framework_forward_plan.md · a_geom_pursuit_programme.md
Geometric freeze: geometric_confinement_s3_geodesic_alternative_freeze.md
1. What is CPT (in one paragraph)?
Confined Photon Topology (CPT) is a working one-force unified-field (UFT) research programme — a documented multi-domain alternative to multi-force SM+QG packaging, with open residuals listed. Charged particles and nuclei are modelled as geometric / topological structures on \(S^3\) (Hopf, Clifford tori, integer windings), with Weber-class electrodynamics as the preferred effective force book and applied tables (nuclear V4, light–matter, etc.) under integrity tags. It is not a completed theory of matter and not a finished TOE certificate. Preferred foundational narrative (A-geom): on round \(S^3(a)\), geodesics are already closed great circles (Hopf fibres / \(T(1,1)\) class); Hopf charge and Clifford/Willmore geometry supply structure and topological stability without first proving Weber force balance. Continuum hold (A-dyn) remains OPEN (Gap 3 / energy residual), not the proof that loops close. Architecture is three books (face ED · face Willmore/generation · bulk mass); generation uses Route E ∥ S⁷ tracks; quarks are SM lobe labels, not free \(e_i\). Public residual chips: hub [cpt-physics.com/status](https://cpt-physics.com/status) (Doctrine v1.1.6). Foot δ is [E INPUT]. Foot K/L is [E] algebra of that input, not a second input.2. What are the main assumptions?
| # | Assumption | Label | |---|------------|--------| | A1 | Free photon @ \(c\) on geodesics + isotropic closed equal period (IPC) ⇒ unique round \(S^3(a)\) among complete simply connected isotropic 3-geometries [E under IPC]. Adopting IPC is conditional_model; ED does not pick geometry. Dynamics = causal Weber-class (Gap 3). | a_geom_gap1_isotropic_photon_containment_uniqueness.md | | A2 | A free quantum is packaged as a null geodesic / Hopf fibre of that geometry | conditional_model | | A3 | Topological charge class is Hopf / linking class in \(\mathbb{Z}\) | conditional_model (+ math once maps exist) | | A4 | Nuclear binding can be organised as multi-α cage + free-\(n\) packing (V4) | conditional_model | | A5 | Applied tables are scored under FT-FIT: sparse anchors, residual science on dense cells | residual_science method | | A6 | Preferred dynamics: causal Weber-class packaging (Maxwell incomplete as confined-photon ontology; used for comparison/bounds). Far static: Coulomb (G3.1). Lab discriminators pre-registered (1064). Single-loop energy check only (G3.3). | conditional_model · Gap 3 · a_geom_force_law_and_gap1_integrity_freeze.md | | A7 | Free electron spin package: cover \(S^3\cong\mathrm{SU}(2)\) ⇒ half-integer type; fundamental irrep ⇒ \(j=\tfrac12\); geometric FD under transport \(\mathcal{T}_{\mathrm{XC}}\) | conditional_model + math under package · §2b |
2b. Electron spin and Fermi–Dirac (human summary)
Q. Does CPT “explain” electron spin? Partly, under explicit packaging — not as an axiom-free miracle.| Step | What you get | Needs packaging? | |------|----------------|------------------| | Ambient core is round \(S^3\cong\mathrm{SU}(2)\) | Double cover of ordinary 3D rotations | IPC / P1 adoption | | Work on the cover, not only \(\mathrm{SO}(3)\) | Half-integer spin representations exist | No — representation theory [E] | | Confined photon seat + director (MSCT) | Single-body \(U(2\pi)=-I\) (spinor monodromy) | Yes — MSCT axioms | | Ground seat = \(T(1,1)\) + fundamental \(\mathbb{C}^2\) | Internal \(j=\tfrac12\) | Yes — \(\mathcal{P}_{j}\) | | Exchange two identical seats (half-turn + rigid co-rotation + director lock) | \(\psi(1,2)=-\psi(2,1)\) | Yes — \(\mathcal{T}_{\mathrm{XC}}\) + assembly |
Q. Is that full quantum field theory fermions? No. Pair exchange phase under geometric axioms is banked; second quantisation, \(N>2\), and relativistic QFT spin–statistics remain open. A parallel literature join is Finkelstein–Rubinstein / Hopfion under an identification dictionary (not automatic). Q. Does electrodynamics choose \(S^3\)? No. Gap 1 is geometry (IPC). Maxwell/Weber are interaction books on the multi-seat exterior (Gap 3 / Appendix D of the compact core draft). Pointers: compact core draft §1b ·a_geom_electron_j_half_fundamental_rep_freeze.md · a_geom_geometric_fd_freeze_v1.md · a_geom_spin_fd_editorial_pass_v1.md.
2c. Pair creation, charge, and hold (human summary)
Q. What is pair production in this geometry language? Creation of two opposite Compton-scale \(S^3\) “bubbles” (local instances): electron and positron seats, not one shared bubble. Under convention SC1, \(e^-\) has \((H,Q)=(-1,-e)\) and \(e^+\) has \((+1,+e)\). Rest energy at least \(2m_ec^2\). Soft free multi-wind light does not become a lone electron by chopping. Q. Does Hopf class explain charge quantisation? It explains discreteness: \(H\in\mathbb{Z}\) is homotopy-stable. Ground free leptons are packaged as unit class \(|H|=1\) with lab charge \(\pm e\). That does not derive the coulomb of \(e\) from pure topology, nor quark fractional charges from integer \(H\) alone. Q. If geometry confines geodesics, is the electron “stable”? Not automatically. IPC / A-geom answers: the ambient can support closed free orbits. Hold (O5 / BN3) asks whether the seat is a long-lived non-radiating fixed point under 3-face electrodynamics — still open. Soft modes in energy checks mean incomplete energy models, not “no electron.” Q. Does the thin-shell exterior model close hold? No. It fixes a useful exterior: Coulomb self-energy \(\alpha/(2R)\) on the match sphere, \(O(\alpha)\) of rest energy at Compton radius. That is boundary-condition packaging for the hold problem, not a stability proof (a_geom_bn3_o5_l1_hold_join_results.md).
Q. What does the H-D hold packaging stack add (compact core v2.10 §1c.3b)?
It poses the residual with a frozen exterior shell, interior nonlocal self-energy plus zero-free dual-density and wire-log walls, energy-conjugate stationarity \(F_\varepsilon=-\partial_\varepsilon U_{\mathrm{nloc}}\), and a discrete FP9 PD proxy. That is packaging, not a continuum hold theorem. Soft modes still mean incomplete functionals, not “no electron.”
Q. Does “dipole-dark” (H-D5) prove the electron holds?
No. H-D5 is a Maxwell/Larmor multipole diagnostic: uniform packaging filters a leading dipole radiation channel under that language. The actual hold residual is a fixed point of the Weber (causal) self-force equation on the closed wind with L1b exterior BC — \(\mathbf F_{\mathrm{self}}=0\) and stability — not \(\mathbf p=0\). A seat can be dipole-dark and still fail self-force stationarity.
Q. Does annihilation prove seats cannot hold?
No. Annihilation is a two-seat channel when \(e^-\) meets \(e^+\). Isolated free electrons in ordinary matter persist; that is the hold question, not the pair-reconnection channel.
Pointers: compact core §1c (incl. §1c.3b) · a_geom_hold_packaging_for_compact_core.md · a_geom_bn4_s0_pair_split_options_freeze.md · a_geom_bn3_s4_closeout_results.md · a_geom_bn3_o5_l1_hold_join_results.md · a_geom_bubble_nucleation_research_arc.md.
2d. Spectrum skeleton vs particle masses (human summary)
Q. Do torus knots on \(S^3\) give the particle mass spectrum? They give a spectrum skeleton: discrete labels \(T(p,q)\), number-theoretic selection (which levels exist), path energies \(\propto 1/\sqrt{p^2+q^2}\), and an isolated ground state \(T(1,1)\) (~37% gap to the next primitive knot). That is real geometry — not the Standard Model mass tower. Q. Is the electron \(T(1,1)\)? Under the sector package: yes as the leptonic ground seat (identity packaging). Spin \(j=\tfrac12\), charge \(\pm e\), and Fermi–Dirac exchange sit on named packages (§2b), not on knot length alone. On the v1 multiplet card (GS-Q1b) the electron row is core-ready: sector L0, freeze force dual packaging \(\approx(0.07,-0.653)\), packaging \(m_{\mathrm{dyn}}\approx 0.342\) (not MeV by itself), and full \(Q/j/\mathrm{FD}\) under packages. Continuum hold is not required for that card. Q. Is the proton \(T(2,3)\)? No as a theorem. \(T(2,3)\) is a hadronic candidate label (crossing number 6 in programme language). Path energy at fixed radius is only ~0.39 of the electron’s — lighter, not heavier. Making a heavy hadron needs a different scale book (e.g. strong-scale bag density), which is imported physics, not pure ED on \(S^3\). On the multiplet card the hadronic row keeps dual pack and dynamical mass as N/A, and charge/spin/statistics open — no silent copy from the electron, and no proton theorem. Q. Are the muon and tau other knots? No under the frozen boundary. Same bag scale + other knots makes them lighter, not ~207× or ~3477× heavier. Intermediate knots such as \(T(1,2)\) are not the muon. Flavour hierarchy is Route E (beyond pure ED knot shopping): a Willmore bending ladder is active for charged-lepton ratios (GS-E1), still with open coefficient origin — not a return to knot shopping. Q. Path energy vs “dynamical mass”? Path energy = mode on a closed curve (Compton ruler under M-PHOT). Dynamical mass = energy of a packaged seat (Weber stack, exterior, walls, binding). For the electron, the default dynamical book is the force dual seat, not the free energy minimum (force and energy packaging differ by ~18%). They must not be swapped to hide open hold or absolute-scale residuals, and packaging units must not be sold as MeV without an identity/unit package. Q. What is the “writing rule” for spectrum claims? Keep columns separate: label · sector · dual pack · path \(\mathcal{G}\) · \(m_{\mathrm{dyn}}\) · sector scale · abs MeV · quantum numbers. Use N/A explicitly. Never blend dual cancel + bag density + knot path into one number sold as a derivation. Never paste the electron dual seat onto a hadron. Q. Does dual cancel prove the electron is stable (hold)? No. Dual cancel is banked seat packaging structure. Continuum hold remains OPEN (deferred). Packaging language does not close the hold theorem. Q. How is absolute \(m_e\) (MeV) handled on the multiplet card? Not from dual cancel. Two honest options: (1) lab \(m_e\) as an identity / check input; (2) soft package \(\mathcal{P}_{\mathrm{EMC}}\): bulk/cosmological Mach mass \(m_{\mathrm{Mach}}(G,H_0,\alpha,\ldots)\), face path energy \(E=\hbar c/a\), glue \(a=\hbar/(mc)\) so \(E=mc^2\) by identification — not a bulk–face theorem. Hard absolute \(a\) without mass remains open (local pure-geometry absolute closed-null). Optional face Weber factor \(\langle S\rangle\approx 1-\frac34\alpha^2\) is fine structure only. Q. Does the card derive \(E=mc^2\)? No. Under \(\mathcal{P}_{\mathrm{EMC}}\) the match is soft packaging. Face confinement energy and Mach mass are linked by choosing \(a\) from \(m\), not by an independent-length theorem. Pointers: compact core §1d–§1d.3 (v2.15) ·a_geom_gap2_gs_q1b_multiplet_card_oh0_results.md · a_geom_o_emc3_package_card.md · a_geom_s7_delta_KL_residual_status.md · a_geom_s7_p_L_effective_length_package_card.md · flavour_heavy_lobe_reframe.md · a_geom_gap2_genuine_spectrum_programme.md · GS-Q1b · GS-E1.
3. Parameter inventory (honesty)
| Item | Status | |------|--------| | Fine-structure constant \(\alpha\) | Input (not derived as free theorem) | | Absolute electron mass \(m_e\) | Soft package \(\mathcal{P}_{\mathrm{EMC}}\) (Mach + face glue) [M]; hard theorem OPEN; not from dual alone | | Nuclear free-\(n\) recipe | Global packing recipe (Slice 7); residual multi-channel separate | | Residual nuclear stack v1 | residual_science flags (R5/U5/U3/MS1); not public stock | | Proton \(6\pi^5\) packaging | Remarkable coincidence / packaging — not full spectrum derivation |
4. What is open (foundational)?
| Gate | Status | Path | |------|--------|------| | Gap 1 — why ambient geometry is \(S^3(a)\) | OPEN (premise \(\mathcal{P}_{S^3}\)) | A-geom primary | | Structure theorems on \(S^3\) (geodesics, Hopf, Willmore) | BANKED under premise | A-geom done | | Continuum hold: \(\delta U=0\), \(\delta^2 U\ge 0\), multi-\(n\) joint | NOT MET · check-only under A-geom (G3.3) · BN3 residual named (§2c) | A-dyn / BN3 | | Free-capture free → confined | CONDITIONAL / outer free OPEN | A-dyn | | Pair product as two opposite \(S^3\) bubbles | Structure banked (§2c); rates open | BN4 / PAIR | | Electron \(j=\tfrac12\) + geometric FD pair phase | Banked under named packages (§2b) | Pathway A | | Two-loop Coulomb asymptotics | Banked under multipole axioms (G3.1) | Gap 3 | | Causal Weber-class packaging | Design frozen (G3.2); not Hopf-derived | Gap 3 | | Absolute scale (local \(m_e\)) | Mass origin banked (confinement \(E_1\)); soft abs \(\mathcal{P}_{\mathrm{EMC}}\) [M]; hard join OPEN | Gap 2 · P4 · O-EMC-3 · core v2.14 | | Spectrum skeleton (labels, isolation, sparsity) | BANKED geometry; SM masses not derived | §1d / G-SPEC | | v1 multiplet card (e core-ready; H structural) | BANKED under packages; proton not theorem; abs MeV not dual-derived | §2d / GS-Q1b | | Dual cancel as seat packaging (not hold) | BANKED structure; hold deferred | FM-3 / §1c.3b | | \(\mu,\tau\) / full flavour hierarchy | Route E ACTIVE (ladder ratios); coeff origin OPEN | GS-E1 · not knot shopping | | S⁷ Foot \(\delta\), Foot \(K/L\) first principles | OPEN · structure banked (hierarchy band, pole, \(L_{\mathrm{eff}}\)); \(\mathcal{P}_L\) optional 2× read [M] only | a_geom_s7_delta_KL_residual_status.md · \(\mathcal{P}_L\) card | | Heavy flavour multiplet membership (FL-HEAVY) | PARKED after H1–H6; quark ≠ free \(e_i\); not Route E | flavour_heavy_lobe_reframe.md |
Table residuals do not close Gaps 1–3. Soft mode does not mean “loops fail to close.”
5. Nuclear prediction API (stock vs residual)
| Call | Mode | Uses residual multi-channel? | Uses measured BE to change BE? | |------|------|------------------------------|----------------------------------| | predictBE / get_isotope (public) | stock | No | No | | predictBE_residual / mode: "residual" | residual | Yes (if flags on) | FreeN gates need measured for freeN/skin |
ft_res_residual_stack_v1_freeze.md.
Illustrative full-table means (393 isotopes, 2026-08-02):
| Mode | mean \|BE %\| | |------|-------------:| | stock | ~0.52% | | residual v1 | ~0.45% |
Residual mean is in-sample residual science, not a blind zero-parameter theorem.
6. Dual track (external contact)
| Track | Goal | Does not mean | |-------|------|-------------------| | FT-RES | Residual patterns under FT-FIT | Electron hold closed | | W-LAB | Pre-registered Weber vs Maxwell lab | Ontology proved until real data under freeze |
Do not wait for hold theorem to run dual track. Do not claim dual-track wins as hold theorem.7. Evidence labels (use in writing)
| Label | Meaning | |-------|---------| | theorem | Math under stated axioms | | conditional_model | Named model / flags / packaging | | residual_science | Residual diagnostics (may use measured anchors for gates) | | empirical | Prospective lab or hold-out under freeze |
Full: evidence_label_taxonomy.md.
8. What we explicitly do not claim
- Complete theory of everything / all particle masses from geometry alone - Continuum confined electron already solved - Nuclear residual stack as blind low-parameter law - Non-dilution / Weber uniqueness without lab controls - Absolute \(G\), \(H_0\), or \(m_e\) as independent free predictions from this core - Biomedical / cosmology mechanism claims as canonical (quarantined) - Electron \(j=\tfrac12\) or Fermi–Dirac without the named packaging (fundamental irrep, RIGID/DIR-LOCK, assembly) - Hadron spin towers “solved” by the electron \(j=\tfrac12\) freeze alone - Torus-knot path energies or universal bag constant as the SM / proton / muon spectrum - \(T(2,3)\) “proved” to be the proton; empty lattice norms as missing PDG particles
9. What is strong enough to keep investigating?
- Coherent \(S^3\) / Hopf / Clifford geometry and process bookkeeping - Explicit banking of failed hypotheses (scalar radiation, hold obstruction, etc.) - Dense applied tables with residual ledgers (FT-FIT) - Public API hygiene: stock vs residual split - W-LAB protocols ready for empirical test
External referee summary (Sol): programme grade C+ (revised); quantitative pattern skill + HOLDOUT_V1 transfer credited; finished-theory / continuum hold still open; not 1,063 solved puzzles — see sol_external_review_takeaways_freeze.md §1b.
10. Where to go next
Living plan: framework_forward_plan.md Frozen residual stack: ft_res_residual_stack_v1_freeze.md Sol alignment: sol_external_review_takeaways_freeze.md Checkable board: framework_checkable_predictions_board.md
a_geom_compact_core_draft.md §1b · a_geom_spin_fd_editorial_pass_v1.md.
Spectrum stack: core §1d–§1d.3 · Q1b card · \(\mathcal{P}_{\mathrm{EMC}}\) · \(\mathcal{P}_L\) · S⁷ residual status · G-SPEC programme.
11. One-line
CPT core FAQ: one-force UFT programme; geometry + open hold; multiplet card e core-ready / H structural; three books; Route E ∥ S⁷ (δ/K/L OPEN, P_L [M]); FL-HEAVY parked; P_EMC soft m [M]; not TOE.