Pith Number

pith:N4BCK4MV

pith:1993:N4BCK4MVZUFHPTWLB5SJBCBPTA

not attested not anchored not stored refs pending

van Vleck determinants: geodesic focussing and defocussing in Lorentzian spacetimes

Matt Visser

arxiv:hep-th/9303020 v1 · 1993-03-03 · hep-th · gr-qc

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N4BCK4MVZUFHPTWLB5SJBCBPTA}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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.

Cited by

3 papers in Pith

Spacetime from Operator Algebras

The Continuum Limit Analysis of Causal Fermion Systems for Curved Spacetimes

Optimal paths across potentials on scalar field space

Receipt and verification

First computed	2026-07-04T15:55:56.479204Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f02257195cd0a77cecb0f6490882f981bd72ac57f55cee1251734834d7d046d

Aliases

arxiv: hep-th/9303020 · arxiv_version: hep-th/9303020v1 · doi: 10.48550/arxiv.hep-th/9303020 · pith_short_12: N4BCK4MVZUFH · pith_short_16: N4BCK4MVZUFHPTWL · pith_short_8: N4BCK4MV

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/N4BCK4MVZUFHPTWLB5SJBCBPTA \
  | 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: 6f02257195cd0a77cecb0f6490882f981bd72ac57f55cee1251734834d7d046d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5cb17d34ce48e4fa1ed5403b4825703a73917ab79d5d0dfed265f5e153e81224",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "",
    "primary_cat": "hep-th",
    "submitted_at": "1993-03-03T17:57:10Z",
    "title_canon_sha256": "5d32cd534781f07c57f53cbad7cfdcdc3e5f252f4fceed27f70084d1a0a64419"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-th/9303020",
    "kind": "arxiv",
    "version": 1
  }
}