Pith Number

pith:4GMGDLJS

pith:2015:4GMGDLJS6LQPTY4Q4H3N3CEZJ7

not attested not anchored not stored refs pending

Entropy in the cusp and phase transitions for geodesic flows

Anibal Velozo, Felipe Riquelme, Godofredo Iommi

arxiv:1511.03967 v2 · 2015-11-12 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4GMGDLJS6LQPTY4Q4H3N3CEZJ7}

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.

Receipt and verification

First computed	2026-05-18T00:05:40.046837Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e19861ad32f2e0f9e390e1f6dd88994fca9adcb0cf45cd9a7e16122655734b12

Aliases

arxiv: 1511.03967 · arxiv_version: 1511.03967v2 · doi: 10.48550/arxiv.1511.03967 · pith_short_12: 4GMGDLJS6LQP · pith_short_16: 4GMGDLJS6LQPTY4Q · pith_short_8: 4GMGDLJS

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/4GMGDLJS6LQPTY4Q4H3N3CEZJ7 \
  | 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: e19861ad32f2e0f9e390e1f6dd88994fca9adcb0cf45cd9a7e16122655734b12

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a3b05b0ed9ab0e23686eede48781369daeab535e5237270abeb60d0fea1757f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-11-12T17:00:31Z",
    "title_canon_sha256": "f09c8a3c4b42ec2bfb513b3593e3fff9c9682d2529d0edab5e7430a3dd1d94a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.03967",
    "kind": "arxiv",
    "version": 2
  }
}