Pith Number

pith:NA74O2R6

pith:2007:NA74O2R63EDUOVH76ZKVEBHEON

not attested not anchored not stored refs pending

Singular surfaces, mod 2 homology, and hyperbolic volume, II

Marc Culler, Peter B. Shalen

arxiv:math/0701666 v7 · 2007-01-24 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NA74O2R63EDUOVH76ZKVEBHEON}

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	2026-05-18T04:39:06.960627Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

683fc76a3ed9074754fff6555204e473488b6900ab19a2e14ae6570b9d15102e

Aliases

arxiv: math/0701666 · arxiv_version: math/0701666v7 · doi: 10.48550/arxiv.math/0701666 · pith_short_12: NA74O2R63EDU · pith_short_16: NA74O2R63EDUOVH7 · pith_short_8: NA74O2R6

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/NA74O2R63EDUOVH76ZKVEBHEON \
  | 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: 683fc76a3ed9074754fff6555204e473488b6900ab19a2e14ae6570b9d15102e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48438123555246b7d57bf54f925ed82fae4536c76593f75c43558b986b4b9190",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2007-01-24T03:16:07Z",
    "title_canon_sha256": "ba077faea24267006fa4f5c95e793b8bb7ce688a157d06fbc6b088c817cbb5f6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0701666",
    "kind": "arxiv",
    "version": 7
  }
}