Pith Number

pith:36Z4QO7G

pith:2012:36Z4QO7GYDJRCUIH2X7JQH3IIF

not attested not anchored not stored refs pending

A 3-Manifold with no Real Projective Structure

Daryl Cooper, William Goldman

arxiv:1207.2007 v2 · 2012-07-09 · math.GT · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{36Z4QO7GYDJRCUIH2X7JQH3IIF}

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	2026-05-18T02:30:08.819194Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dfb3c83be6c0d3115107d5fe981f684145c17e8f56b9c96226f552555fd47a45

Aliases

arxiv: 1207.2007 · arxiv_version: 1207.2007v2 · doi: 10.48550/arxiv.1207.2007 · pith_short_12: 36Z4QO7GYDJR · pith_short_16: 36Z4QO7GYDJRCUIH · pith_short_8: 36Z4QO7G

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/36Z4QO7GYDJRCUIH2X7JQH3IIF \
  | 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: dfb3c83be6c0d3115107d5fe981f684145c17e8f56b9c96226f552555fd47a45

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d27767d8ecc3865732100cb23ac2172f9c9c4beb4d6beec70fdd59ffc23ac7d2",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-07-09T11:23:28Z",
    "title_canon_sha256": "b24921696d5bb8668759c156d2131ca156ddf0837654e1a0668208e27534de48"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.2007",
    "kind": "arxiv",
    "version": 2
  }
}