Pith Number

pith:GXVZN7BG

pith:2012:GXVZN7BG73R2IPBUEHUSIG3MFE

not attested not anchored not stored refs pending

Trisecting 4-manifolds

David T. Gay, Robion Kirby

arxiv:1205.1565 v3 · 2012-05-08 · 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{GXVZN7BG73R2IPBUEHUSIG3MFE}

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	2026-05-18T00:53:26.428475Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35eb96fc26fee3a43c3421e9241b6c2919ab3343849ca83d36fe5ef4a26abaf8

Aliases

arxiv: 1205.1565 · arxiv_version: 1205.1565v3 · doi: 10.48550/arxiv.1205.1565 · pith_short_12: GXVZN7BG73R2 · pith_short_16: GXVZN7BG73R2IPBU · pith_short_8: GXVZN7BG

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/GXVZN7BG73R2IPBUEHUSIG3MFE \
  | 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: 35eb96fc26fee3a43c3421e9241b6c2919ab3343849ca83d36fe5ef4a26abaf8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c8d322c26b11015ffa08ea6fc4d0d7fd66d62477cb702e4d810cd4535f8dd2d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-05-08T00:36:06Z",
    "title_canon_sha256": "2e621e8bfe2470d50dce9ecc682d8c005bdaf2bcd0c987f9119ac5dbc965b60e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.1565",
    "kind": "arxiv",
    "version": 3
  }
}