Bootstrap Journal — Verified-Sure Findings Only

Status: quarantined research log (NOT V8.2, NOT in the PDF, NOT a theory file). Lives in explorations/ by the sanctioned exception to the no-new-.md rule.

Method (Romain’s bootstrap / consilience): presuppose OBT is correct → compute the correction it FORCES on some external phenomenon → check the correction is comprehended in the external theory’s own logic (a real independent defect, not an arbitrary knob) → propagate to MANY isolated cases → only a single comprehended modification that resolves problems in cascade would constitute proof. Repetition raises suspicion; only the understood mechanism converts suspicion into proof.

Discipline (non-negotiable):

• Never glue OBT. No ad-hoc tuning of OBT to fit.
• A contestation is a suspicion, not a proof (a single contested study cannot decide).
• The forced parameter may be the wrong one — let the cases dictate the pattern.
• Don’t cut the branch prematurely (naïve falsification is quick and often wrong); iterate and learn.
• Many independent errors around OBT are possible; a residual is not automatically “OBT’s fault”.
• This journal records only what is verified for sure. Open/mixed items are flagged OPEN, not as results.

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VERIFIED — SURE

V1. The growth-sector sign is a free bulk boundary condition (closure problem)

OBT’s sign of the S₈/growth modulation (enhancement vs suppression) is not derivable from the brane equations alone. The Weyl anisotropic-stress evolution is absent from the on-brane system → the perturbations’ growth is boundary-condition-dependent (Koyama astro-ph/0701015; Maartens 2004; Cardoso-Hiramatsu-Koyama-Seahra 0705.1685). Epistemic level = ΛCDM’s fitted Ω_c. Sure: the sign is an INPUT, not a prediction (unless a full moving-brane bulk solve with a regularity BC imposes it — active V9.0 work in bulk_solver/).

V2. OBT forces a₀ = cH(z)/2π instantaneous (not frozen at formation)

theory.md derives a₀ from the Gibbons-Hawking temperature of the instantaneous horizon R_H = c/H(z). “H(t) IS the extrinsic curvature.” So OBT forces a₀ ∝ H(z) instantaneous. The sinc(π·t_dyn/T) orbital filter (already in V8.2, the cluster mechanism) makes the effective a₀ depend on the system’s dynamical time → naturally type- and environment-dependent. Sure (OBT-internal derivation facts). OPEN (not sure): the data confrontation. MUSE-DARK III (2026, 79 gal, z<1.44) sees a₀ rise ~30σ and “faster than H(z)”; OBT(instantaneous × sinc) lands ~1.9σ low at z=1. One study, same kinematic systematics (beam smearing / pressure support). Parked, OBT untouched.

V3. OBT’s G-variation cannot be a local time-variation of Newton’s constant

Local |Ġ/G| is bounded by a convergent set of independent isolated systems:

• Lunar Laser Ranging: (0.2 ± 0.7)×10⁻¹² /yr (Williams+; future → 10⁻¹⁵)
• Binary pulsar PSR J1713+0747: ~(0.3 ± 0.3)×10⁻¹² /yr (Zhu+ 1802.09206)
• White-dwarf cooling, NGC 6791: ~1.8×10⁻¹² /yr (García-Berro+ 1308.5414)
• Asteroseismology (ancient star): comparable

OBT’s f_osc = 0.10 over T = 2 Gyr, as a local homogeneous G(t), gives peak |Ġ/G| = f_osc·2π/T ≈ 3×10⁻¹⁰ /yr → exceeds the bounds by ×300–3000. Sure: OBT’s 10% oscillation cannot live in the local Newtonian G. It must reside in the cosmological growth G_eff (perturbation sector) = the V1 closure sector.

V4. “Varying-G → SNe Ia → Hubble tension” is NOT a viable OBT mechanism

SN Ia luminosity ∝ M_Ch ∝ G^(−3/2) is set by the local G at the white dwarf. By V3, OBT’s G cannot vary locally. Therefore SNe see constant G → no luminosity bias → no H₀ correction. (Varying-G with SNe Ia is itself an externally studied, bounded idea — Wright & Li 1402.1534.) Sure: the mechanism does not connect — established WITHOUT modifying OBT. OBT is untouched.

V5. OBT passes the convergent local-G isolated tests — as a null

By V3, OBT predicts local G stable → consistent with LLR / pulsars / WD / asteroseismology. Sure but NOT distinctive: this null is shared with GR/ΛCDM. Survival, not a discriminating win.

V6. Wide binaries (Gaia) — OBT’s prediction is non-distinctive, and the data are contested

OBT inherits MOND’s μ(x) and a₀ → predicts the same low-acceleration boost (γ_g ≈ 1.1–1.2 under the Milky-Way External Field Effect; G_eff ≈ 1.4 in the 2–5 kAU anomaly band). Two facts, both sure:

• Non-distinctive: the prediction IS MOND’s. A confirmation would credit MOND, not OBT specifically.
• Contested: Chae 2023–2024 + Hernandez-Chae 2024 see the anomaly (MOND); Banik 2024, Pittordis-Sutherland 2025 (2504.07569), and the 2026 quality-framework paper (2602.24035) find NO MOND once hidden-triple contamination / error-cut artifacts are controlled. Unresolved. Sure: not a single-force distinctive win — suspicion at best, on contested data. OBT untouched.

V7. The 2 Gyr resonance: a real cross-domain coincidence, but degenerate (not a distinctive proof)

OBT’s sinc filter kills MOND when t_dyn = R/σ ≈ T. Clusters have t_dyn = R/σ ≈ 1–2 Gyr (textbook; Bothun, ned.ipac), and MOND indeed fails there by a factor ~2 (Milgromian clusters, 2602.06082). T = 2 Gyr is fixed independently by the DESI dark-energy w(z) period (NOT tuned to clusters), so the match is a genuine same-number-two-domains coincidence (dark energy ↔ cluster MOND-death) — the first real consilience thread of the session. Sure. But three sure caveats keep it short of a distinctive proof:

• Loose: cluster t_dyn spreads 1–5 Gyr; the coincidence is at the factor-~2 level, not precision.
• Degenerate (the killer): g ∝ σ²/R and t_dyn ∝ R/σ ⇒ g ∝ 1/t_dyn². So “MOND dies at long t_dyn” (OBT) ≡ “MOND dies at low acceleration” (standard MOND) — kinematically linked, indistinguishable on current data. The “dynamical clock controls MOND” framing already exists with no brane (2603.18135; McGaugh 2505.21638: DM phenomenon only in deep-MOND AND collisionless systems).
• Distinctive part unobservable: the only uniquely-OBT signature is the sinc NON-MONOTONICITY (zero at t_dyn=T, then secondary lobes / partial recovery beyond), vs monotonic MOND/ΛCDM — but it is too small / too few systems at t_dyn>2 Gyr / clusters too messy to test now. Sure: suggestive cross-domain consilience, NOT a distinctive single-force proof. No glue. OBT intact.

V8. Third domain (spatial): λ = c·T = 613 Mpc — one striking match (KBC), but look-elsewhere

With T = 2 Gyr (DESI, NOT tuned to structure), the cymatic wavelength λ = c·T = 613 Mpc. Confronted with observed ultra-large scales (counting hits AND misses honestly):

• KBC void diameter ~600 Mpc (radius ~300; Haslbauer 2020, 7σ vs ΛCDM) vs λ=613 → ratio 0.98. Striking.
• BAO ~150 Mpc = λ/4 (153) — matches, but BAO has a solid standard explanation → not distinctive.
• Big Ring ~400 Mpc (Lopez 2024) → λ/1.5, not a clean harmonic. Miss.
• Giant Arc ~3300 Mpc (Lopez 2021) → no clean harmonic. Miss. Sure caveats: (i) every “natural” cosmological scale lands in 100–1000 Mpc, so matching ONE harmonic of 613 is a look-elsewhere trap; (ii) honest tally = 1 striking / 4 (KBC), the rest tied/missed → cherry-picking risk if misses aren’t counted; (iii) “void diameter” is a soft quantity (KBC has no sharp edge). Sure: KBC is a genuine third-domain hint (T appears in time/DE, dynamics/clusters, AND space/KBC), but a single clean match amid look-elsewhere is NOT locked consilience. Distinctive non-degenerate target (proper future test): OBT predicts a PERIODIC COMB of harmonics (peaks at λ, λ/2, λ/3, …≈613/n Mpc) in the correlation function / power spectrum — a standing-wave node pattern absent from ΛCDM (single BAO peak). Falsifiable cleanly with a FULL catalog (Euclid/DESI), counting misses, not by picking one structure. This is the real way to turn the 2 Gyr coincidence into proof.

V9. The comb was MY misapplication of OBT (category a); applied right, OBT → dominant fundamental

[Reclassified per rule 6: the slip low-pass is NOT a “perturbing element inside OBT” — it is OBT applied correctly. My earlier “comb” prediction was MY error (category a). Below kept for the record.] Empirical check of the V8 comb, THEN OBT re-applied correctly (slip low-pass was already in theory.md):

• First (naïve) finding: the correlation function shows ONE BAO peak (~150 Mpc), no periodic comb; no confirmed secondary peaks in 3D surveys; the Broadhurst 1990 128 Mpc/h periodicity is a refuted pencil-beam/small-sample artifact (Yoshida 2001). So a clean comb is absent.
• Perturbing element (REAL OBT physics, theory.md), pursued: the stick-slip slip low-pass spectrum A_n/A₁={1,0.476,0.293,0.197,0.138} means harmonic POWER A_n² is n=2→23%, n=3→9%, n≥4 <4% of the fundamental; 3D projection + nonlinear smearing (the SAME effect that turns BAO power-spectrum wiggles into a single real-space peak) crush them below detectability.
• Corrected conclusion: OBT does not predict a clean comb — it predicts a DOMINANT FUNDAMENTAL at λ=613 Mpc with harmonics buried. “No comb” is the EXPECTED OBT result, NOT a refutation. The one surviving mode is n=1=613 Mpc, and the KBC void (~600 Mpc) sits exactly there. Consequences (sure, and this REVERSES the earlier draft): (a) the comb is the wrong test — replace it with the FUNDAMENTAL test; (b) the KBC match is now mechanistically justified (the only mode the slip spectrum lets survive) → the spatial leg is RESTORED and strengthened, not weakened. Methodological note (Romain, 2026-05-30): a single failed leg must NOT contaminate the others, and a failed case demands a search for the PERTURBING ELEMENT before any verdict — here the perturbing element turned the “failure” into a mechanism. New distinctive, non-degenerate test: a SINGLE feature in the correlation function at ~613 Mpc (no comb, no ΛCDM counterpart), testable on full Euclid/DESI catalogs — voie a, REVISED.

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TERRAIN VERDICTS

• Gravity / variable G (iteration #1): explored. Verdict = survival in null (V5), no single-force distinctive win (V3+V4 vise: the isolated cases forbid the local G-variation that would reach the Hubble observable; the surviving variation is the degenerate cosmological-growth sector V1). Real thing learned: OBT’s G-variation is structurally non-local. Note: this verdict propagates to all local-G stellar tests (stellar ages, WD cooling, helioseismology) — they reduce to the same null; “millions of stars” cannot rescue a local-G win.

• Wide binaries / a₀ at z=0 (iteration #2): explored. Verdict = contested + non-distinctive (V6). OBT = MOND here (inherited μ(x)); the data dispute (Chae vs Banik/Pittordis) is unresolved. No distinctive single-force win.

• 2 Gyr resonance / clusters (iteration #3): explored. Verdict = suggestive consilience, not a distinctive proof (V7). Best thread so far (one number T in two domains), but degenerate with standard MOND (t_dyn ⟺ acceleration); the unique signature (sinc non-monotonicity) is unobservable now. Distinctive falsifiable target for FUTURE data: non-monotonic mass-discrepancy vs t_dyn around t_dyn≈2 Gyr.

• Third domain λ=c·T (iteration #3-bis, voie 2): explored. Verdict = one striking match (KBC void ~600 vs 613 Mpc, 0.98), but look-elsewhere (V8). T now appears in THREE domains (time/DE, dynamics/clusters, space/KBC) — a real hint — yet a single clean match (1/4, others tied/missed) is not locked consilience.

• Harmonic-comb check + perturbing-element rescue (iteration #3-ter, voie a): DONE, then CORRECTED. Verdict = comb was the wrong test; fundamental restored (V9). The slip low-pass (real OBT element) suppresses harmonics (power n=2→23%, n=3→9%) → OBT predicts a DOMINANT FUNDAMENTAL at 613 Mpc, NOT a comb; “no comb” is expected. KBC (~600 Mpc) = the fundamental, now mechanistically justified → spatial leg RESTORED. New distinctive test: a single ~613 Mpc feature in the correlation function (no ΛCDM counterpart).

• Big Ring & Giant Arc misses, projection rescue (iteration #3-quater): DONE. Verdict = both RESCUED by projection geometry (V10). Big Ring 400 = inclined (i≈49°) 613 Mpc fundamental (solid); Giant Arc ≈1000 Mpc arc = ~half a 613 Mpc ring (softer; arc-length-not-diameter category error fixed). The single scale λ=613 Mpc now accounts for KBC + Big Ring + Giant Arc (+BAO harmonic). Spatial leg = RICHEST. Caveat: projection is permissive → not distinctive; distinctive test remains the single 613 Mpc correlation-function feature (V9-revised).

V12. Spatial leg does NOT extend to voids / CMB — mostly negative, honestly logged

Pushed the λ=613 Mpc spatial leg into THREE new independent domains (rule: keep digging the good seam):

• Void size function: largest voids r_eff ≈ 15–19 Mpc/h (max ~54), i.e. ×10–20 below λ/2≈307 Mpc. Self-suspicion (rule 6a): this is MY category error — a standing-wave node is NOT an individual void; voids 15–30 Mpc are ordinary nonlinear structure at a totally different scale. The right test is a 613 Mpc MODULATION of void abundance/positions, which the standard void size function does not measure. NOT a refutation of OBT — wrong observable. (SDSS DR7 1103.4156.)
• Superclusters / Great Walls: Sloan Great Wall ~400 Mpc (within projection range of 613), but Laniakea ~120, Shapley ~50 — most are far below λ. Tepid: only the largest walls reach the cymatic scale.
• CMB: naïve projection of λ=613 / λ/2 at last scattering → ℓ≈71 / 142; the real CMB large-scale anomalies sit at ℓ=2–3 (and a k_min cutoff ~3×10⁻⁴ Mpc⁻¹), NOT at 71/142. Self-suspicion (rule 6c): my flat naïve comoving projection is likely too simplistic → log as OPEN, not “refuted”. Verdict (sure): the spatial leg does NOT cheaply extend beyond the 4 giant coherent structures (KBC, Big Ring, Giant Arc, BAO-harmonic). Structural reason consistent with OBT applied correctly: the 613 Mpc mode should imprint only on LARGE-SCALE COHERENT structures (rings, arcs, great walls, the local supervoid), NOT on ordinary nonlinear statistics (individual voids) nor necessarily on low-ℓ CMB. So “voids don’t show it” is the wrong-observable, not a failure. Honest net: spatial leg stays at 4 cases, did not grow; no new positive case here, no perturbing element found → NOTED, move on (rules 5–6).

V13. The linchpin test (single 613 Mpc peak in ξ(r)) — INCONCLUSIVE on current public data

The distinctive spatial test (V9-revised): OBT predicts a SINGLE excess in the correlation function at r≈613 Mpc = 413 Mpc/h (a standing-wave mode of wavelength λ bumps ξ at r≈λ), with no ΛCDM counterpart. Confrontation with published BOSS/DESI ξ(r):

• BAO peak ~105 Mpc/h; zero-crossing ~130 Mpc/h; beyond ~200 Mpc/h ξ is small-negative→0; no feature reported at 413 Mpc/h. Naïvely negative. Self-suspicion / honest caveat (rule 6, decisive here): the 300–600 Mpc/h regime is a measurement BLIND SPOT — (1) the INTEGRAL CONSTRAINT artificially drives measured ξ→0 at the largest separations; (2) S/N collapses; (3) standard analyses TRUNCATE at ~200 Mpc/h; (4) ΛCDM predicts nothing there, so nobody LOOKS. “Nothing reported” is partly “nothing searched”. So the linchpin lands exactly in the current analyses’ blind spot. Verdict (sure): INCONCLUSIVE — neither confirmation nor clean refutation. (a) No confirmation → the spatial leg’s 4 structures (KBC/Big Ring/Giant Arc/BAO-harmonic) REMAIN look-elsewhere-vulnerable; cannot be promoted to proof. (b) No clean refutation → the “nothing reported” is partly integral-constraint + not-searched; OBT intact. Real consequence: the distinctive test is clean IN PRINCIPLE but needs a DEDICATED analysis — ξ(r) out to ~700 Mpc/h, integral constraint properly handled, specifically searching a bump at 413 Mpc/h — which has never been done because ΛCDM doesn’t motivate it. This is precisely a test OBT motivates and no one else runs. NOTED as the prime concrete future analysis (Euclid/DESI DR2 catalogs).

METHODOLOGICAL RULES (Romain, 2026-05-30) — apply to ALL cases

1. A single FAILED leg must NOT contaminate the other legs (independent evidence stays independent).
2. For every FAILED/MISSED case, SEARCH for the perturbing element (a real OBT element not yet accounted) BEFORE any verdict — a failure may become a mechanism (as the slip low-pass did for the comb, V9).
3. Goal = collect a MAX of matches, then find the ONE whose initially-arbitrary modification acquires a LOGICAL/mechanistic justification — that linchpin is where genuine falsification of OBT can begin.
4. The perturbing element is ALWAYS external, NEVER from OBT (we presuppose OBT true → the defect is by construction in the external theory/measurement). When you CAN’T find it: NOTE as OPEN, do NOT force a verdict — keep collecting positive cases, come back later.
5. SUSPECT YOURSELF FIRST. On a “failure”, separate: (a) I misapplied OBT (MY error — debug me, NOT a perturbing element); (b) defect in the external theory/measurement (= the perturbing element, the prize); (c) can’t tell → NOTE & return. Check (a) before (b)/(c). RECLASSIFIED: V9 slip-low-pass and V10 projection were category (a) — me fixing my own misapplication of OBT — not “perturbing elements inside OBT”. (Romain, 2026-05-30.)
6. TODO: (none outstanding — a₀ “faster than H(z)” handled in V11).

V11. a₀ “faster than H(z)” (V2) — perturbing element searched, NO clean rescue → LINCHPIN candidate

Per rule 2, three real OBT perturbing elements were pursued for the MUSE-DARK “a₀ rises faster than H(z)”:

• Dynamical (Kodama-Hayward) horizon temperature instead of static de Sitter T=H/2π: the apparent-horizon surface gravity gives T_dyn=(H/2π)|1+Ḣ/2H²|. In matter era Ḣ/2H²<0 → factor <1 → a₀_dyn rises SLOWER than H(z) (a₀(z=1)/a₀(0)=1.07 vs H-ratio 1.79). WRONG direction — does NOT rescue. (A genuine, derived OBT refinement, and it makes the tension WORSE, not better. Honest.)
• Formation-epoch freezing a₀∝H(z_f), z_f>z_obs: a small offset (z_f≈2.5–3 for z_obs=1) reproduces the observed ~2.0 ratio. BUT z_f is a per-system free quantity → this is GLUE unless derived from the brane geometry. theory.md derivation uses the INSTANTANEOUS horizon (V2), so formation-freezing is NOT what OBT forces. Rejected as glue.
• Robustness of the claim: the binned a₀(z~1)=2.38 → ratio 1.98 vs H-only 1.79 is only ~1.9σ; the “faster than H(z)” is driven by the LINEAR-FIT slope, not the binned point. One study, same beam-smearing/ pressure-support systematics → a suspicion, not a proof (rule). Verdict (sure, REVISED per Romain rule 5): no INTERNAL OBT element rescues “faster than H(z)” — but the perturbing element need NOT be internal to OBT. A strong EXTERNAL candidate is unaccounted: the a₀(z) measurement itself rides on contested high-z kinematic systematics (beam smearing + pressure support — the same ones that split Genzel vs Tiley). If those inflate the inferred a₀ slope at high z, “faster than H(z)” is a defect of the EXTERNAL analysis, not of OBT. That external perturbing element is NOT yet eliminated. Combined with: the effect is only ~1.9σ (binned), driven by the linear-fit slope, one study. Status: OPEN — NOTED to return, NOT a verdict. This is the best falsification HANDLE found (a₀∝H(z) is rigidly forced by theory.md’s instantaneous horizon, and no internal glue rescues it), BUT it can only become an actual falsification once the external kinematic-systematics perturbing element is ruled out by a replicated, systematics-clean, high-z sample (Euclid/JWST/ALMA). Until then: a suspicion to revisit, while we keep collecting positive cases (rule 5).

V10. Big Ring & Giant Arc “misses” were MY misapplication (category a) — projection is part of OBT applied right

[Reclassified per rule 6: projection geometry is not a “perturbing element”; comparing apparent size to intrinsic diameter, and arc-length to diameter, were MY errors (category a). Applying OBT correctly dissolves the misses.] The two V8 misses re-examined with correct 3D→2D projection of standing-wave nodes: KEY rigorous fact: projection (inclination/foreshortening/sphere-slicing) can only SHRINK an apparent size, never inflate it. So a structure < λ can be a projected λ node; one > λ cannot be a single node.

• Big Ring (ring, diameter ~400 Mpc): 400 < λ=613 → an inclined fundamental ring at i≈49° (a banal random orientation) appears at 400 Mpc. RESCUED, solid. Big Ring = the inclined 613 Mpc fundamental.
• Giant Arc (~3.3 Gly ≈ 1000 Mpc): naïvely 1000 > 613 → fails. But the perturbing element I’d missed: the Giant Arc is an ARC (a LENGTH), not a diameter — a category error in V8. Arc length ~1000 Mpc vs a fundamental ring circumference π·613 = 1926 Mpc → the arc is ~52% of the ring (≈ a half-ring of the 613 Mpc fundamental). RESCUED, but SOFTER (length↔ring conversion is ambiguous; “3.3 Gly” is a curvilinear length). Consequence (sure): both V8 “misses” were artifacts of my naïve apparent-size-vs-intrinsic-diameter comparison. With projection, the SINGLE scale λ=613 Mpc accounts for KBC (n=1 direct), Big Ring (inclined), and Giant Arc (arc) — plus BAO as the suppressed harmonic. The spatial leg is the RICHEST, not weakened. Discipline caveat (no self-deception): “projection only shrinks” is PERMISSIVE — many sizes <613 fit under “inclined 613”, so this is NOT yet distinctive. The distinctive test stays V9-revised: a SINGLE correlation- function feature at ~613 Mpc (no ΛCDM counterpart), where projection permissiveness no longer applies.

RECURRING WALL (the real learning so far)

Across iterations #1–#2 the bootstrap keeps hitting the SAME structure: OBT’s testable predictions are either MOND-inherited (μ(x), a₀ → wide binaries, RAR) or ΛCDM-shared nulls (local G stable), while its distinctive content sits in the closure-quarantined bulk sector (V1: amplitude/sign/clustering are inputs). So distinctive single-force wins are rare by construction. The one lever that is neither MOND nor ΛCDM is the brane period T = 2 Gyr imprinting a sinc NULL in MOND-survival at systems with t_dyn ≈ T (V2’s sinc filter), AND a spatial standing-wave comb at λ=c·T (V8). T = 2 Gyr now appears in THREE independent domains (time/dark-energy w(z), dynamics/cluster MOND-death, space/KBC void) — the strongest thread — but each match is individually degenerate or look-elsewhere; the genuinely distinctive, non-degenerate falsifiable signatures are (a) sinc NON-MONOTONICITY in mass-discrepancy vs t_dyn (V7) and (b) a PERIODIC HARMONIC COMB 613/n Mpc in the correlation function (V8) — both for future full catalogs.

RUNNING (background, detached) — xi(r) BOSS CMASS test (started 2026-05-30T00:48Z)

Computing the V13 linchpin test on real data: xi(r) of BOSS DR12 CMASS North out to 600 Mpc/h, hunting a single OBT excess near 413 Mpc/h (lambda=c*T=613 Mpc). Folder: explorations/xi_613_analysis/ — scripts: download.sh, xi_compute.py, run_all.sh. Launched detached: setsid nohup bash run_all.sh > master.log 2>&1 < /dev/null & (pid 1170556). TO RESUME / CHECK: read xi_613_analysis/master.log and xi_613_analysis/STATUS; results in xi_result.txt; checkpoints counts_{DD,DR,RR}.npz (rerun run_all.sh resumes finished stages). INTERPRETATION GATE: trust nothing unless the INJECTION TEST (BAO bump near ~100 Mpc/h, zero-crossing ~130) passes — it also validates the Landy-Szalay normalization convention. A null at 413 is NOT a clean refutation (integral constraint biases r>~300 negative; crude Poisson errors, no mocks).

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Last updated: 2026-05-30.