Pith Number

pith:XWYQPM4A

pith:2025:XWYQPM4AGB276L5FLT225NEEQE

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Geodesic structure of spacetime near singularities

Dawood Kothawala, Mayank

If the base point is a spacetime singularity, Synge's world function and van Vleck determinant change their scaling to capture non-trivial geodesic flows.

arxiv:2512.12271 v3 · 2025-12-13 · gr-qc · math-ph · math.MP

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We show that, if P is a singular point, the scaling behavior of these bi-scalars changes drastically, capturing the non-trivial structure of geodesic flows near singularities.

C2weakest assumption

That Synge's world function and van Vleck determinant remain well-defined and admit meaningful scaling expansions when the base point P is a spacetime singularity.

C3one line summary

Near spacetime singularities, Synge's world function and van Vleck determinant exhibit drastically altered scaling that reveals non-trivial geodesic flow structures.

References

23 extracted · 23 resolved · 6 Pith anchors

[1] Matter-dominated FLRW spacetime Coincidence : ∆(t, T) = 1 + ϵ2 9T 2 +O(ϵ 3) (17) Singularity : ∆(t, T) =− ℓ2t 972T 5/3t4/3 0 − ℓ2t 243T 4/3t4/3 0 + t 27T 1− ℓ2(t/t4 0)1/3 4t +...(18)

[2] Radiation-dominated FLRW spacetime Coincidence : ∆(t, T) = 1 + ϵ2 8T 2 +O(ϵ 3) (19) Singularity : ∆(t, T) = ℓ2t3/2(5−2 log(t/T)) 4T 5/2t0(log(t/T)) 6 + t T 3/2 1 (log(t/T)) 3 +...(20) The different di

[3] Matter-dominated FLRW spacetime Coincidence :2∆ 1/2(t, T) = 2 9T 2 (23) Singularity :2∆ 1/2(t, T)≃ 2267 2187 √ 21t2 (24)

[4] ∞X k=0 −1/2 k I2k(t′)α2k # dt′a(t′) (α2 +a 2(t′))3/2 = Z t T

[5] H. A.Buchdahl, Gen. Relativ. Gravit.3, 35 (1972) 1972

Receipt and verification

First computed	2026-05-20T00:03:00.335591Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bdb107b3803075ff2fa55cf5aeb484812430a562853bdb5d27b70b4b671ad874

Aliases

arxiv: 2512.12271 · arxiv_version: 2512.12271v3 · doi: 10.48550/arxiv.2512.12271 · pith_short_12: XWYQPM4AGB27 · pith_short_16: XWYQPM4AGB276L5F · pith_short_8: XWYQPM4A

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/XWYQPM4AGB276L5FLT225NEEQE \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: bdb107b3803075ff2fa55cf5aeb484812430a562853bdb5d27b70b4b671ad874

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca0ac7759a1018c70642e9d5dc0e442ae77fc6312ec05840ea0c6118a1405f63",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2025-12-13T10:26:10Z",
    "title_canon_sha256": "03ccff7b7268ba31688d99091052936305f7dc8833a0dd6ab3ea2442bd183c4a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.12271",
    "kind": "arxiv",
    "version": 3
  }
}