Pith Number

pith:I6TVGEKS

pith:2025:I6TVGEKS53YPFYETG6DFTMSEUJ

not attested not anchored not stored refs pending

Hyperbolicity, topology, and combinatorics of fine curve graphs and variants

Roberta Shapiro

arxiv:2501.18705 v1 · 2025-01-30 · math.GT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I6TVGEKS53YPFYETG6DFTMSEUJ}

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

Large flats in large subgraphs of fine curve graphs

Receipt and verification

First computed	2026-07-05T10:07:50.284909Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47a7531152eef0f2e093378659b244a26da5e37cb8ad510155485749fe8874da

Aliases

arxiv: 2501.18705 · arxiv_version: 2501.18705v1 · doi: 10.48550/arxiv.2501.18705 · pith_short_12: I6TVGEKS53YP · pith_short_16: I6TVGEKS53YPFYET · pith_short_8: I6TVGEKS

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/I6TVGEKS53YPFYETG6DFTMSEUJ \
  | 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: 47a7531152eef0f2e093378659b244a26da5e37cb8ad510155485749fe8874da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a1b2c2ec41367870cd99a15e65d2bf7d460a1b803a5425f2f82a56ab8c02016",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2025-01-30T19:05:34Z",
    "title_canon_sha256": "2ebe497da25c6c59887ecb91fc7fc5a9908baeb3d3dcfdaa83f86de415122333"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.18705",
    "kind": "arxiv",
    "version": 1
  }
}