Pith Number

pith:IG4IOIW2

pith:2024:IG4IOIW2SWJ6JIDR64IALGFQKW

not attested not anchored not stored refs pending

Bounds for Lyapunov exponent of circular light orbits in black holes

Emanuel Gallo, Thomas M\"adler

arxiv:2412.10328 v3 · 2024-12-13 · 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{IG4IOIW2SWJ6JIDR64IALGFQKW}

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

1 paper in Pith

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions

Receipt and verification

First computed	2026-07-05T10:32:35.486185Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

41b88722da9593e4a071f7100598b055bc21c1d29691cea281e5ecfe1b496aa1

Aliases

arxiv: 2412.10328 · arxiv_version: 2412.10328v3 · doi: 10.48550/arxiv.2412.10328 · pith_short_12: IG4IOIW2SWJ6 · pith_short_16: IG4IOIW2SWJ6JIDR · pith_short_8: IG4IOIW2

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/IG4IOIW2SWJ6JIDR64IALGFQKW \
  | 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: 41b88722da9593e4a071f7100598b055bc21c1d29691cea281e5ecfe1b496aa1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "798318853ad6ace1bc01da729df7b3c7cf02dace2c26fa5de48d5910e8d8252a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2024-12-13T18:07:08Z",
    "title_canon_sha256": "d3d5772537da1dd5dddbb01eb3e5e72dc306efbef70fc74d502e0b6859366479"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.10328",
    "kind": "arxiv",
    "version": 3
  }
}