Pith Number

pith:ZF2Q263B

pith:2012:ZF2Q263BBGGY65TNT2SXE6SYRQ

not attested not anchored not stored refs pending

Counting arcs in negative curvature

Fr\'ed\'eric Paulin, Jouni Parkkonen

arxiv:1203.0175 v2 · 2012-03-01 · math.DS · math.DG · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZF2Q263BBGGY65TNT2SXE6SYRQ}

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	2026-05-18T03:26:20.808274Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9750d7b61098d8f766d9ea5727a588c2849f22c18a60dedad2bb42785092b2b

Aliases

arxiv: 1203.0175 · arxiv_version: 1203.0175v2 · doi: 10.48550/arxiv.1203.0175 · pith_short_12: ZF2Q263BBGGY · pith_short_16: ZF2Q263BBGGY65TN · pith_short_8: ZF2Q263B

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/ZF2Q263BBGGY65TNT2SXE6SYRQ \
  | 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: c9750d7b61098d8f766d9ea5727a588c2849f22c18a60dedad2bb42785092b2b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd74dea7d785962d02fe20a58a479613f2599cf030c9d136fb3b97ea92bdd4b7",
    "cross_cats_sorted": [
      "math.DG",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-03-01T13:09:11Z",
    "title_canon_sha256": "61dba25bbdeda98d3a49b929b14a8a8464499ef6635d7f378cb3afc09d83d667"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.0175",
    "kind": "arxiv",
    "version": 2
  }
}