Pith Number

pith:ZMVWSGUI

pith:2009:ZMVWSGUI4SRMLKIQ6EBDGFFTTR

not attested not anchored not stored refs pending

The Milnor degree of a three-manifold

Paul Melvin, Tim Cochran

arxiv:0902.1731 v2 · 2009-02-10 · 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{ZMVWSGUI4SRMLKIQ6EBDGFFTTR}

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	2026-05-18T02:58:10.678962Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb2b691a88e4a2c5a910f1023314b39c533add67545f53bdcff4c1ef0e962f8a

Aliases

arxiv: 0902.1731 · arxiv_version: 0902.1731v2 · doi: 10.48550/arxiv.0902.1731 · pith_short_12: ZMVWSGUI4SRM · pith_short_16: ZMVWSGUI4SRMLKIQ · pith_short_8: ZMVWSGUI

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/ZMVWSGUI4SRMLKIQ6EBDGFFTTR \
  | 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: cb2b691a88e4a2c5a910f1023314b39c533add67545f53bdcff4c1ef0e962f8a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e1124cb6ec82e9e371dc61c0bee7b039bdbae57319c709fe4738da13d9d2862a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-02-10T20:16:16Z",
    "title_canon_sha256": "33af395ce44b31d3f7813fc14859ac22b8264c014c9409403c5ae271a10bc0df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.1731",
    "kind": "arxiv",
    "version": 2
  }
}