Pith Number

pith:J7BE7URR

pith:2011:J7BE7URRK7OVDOBPTGF7OX7AOG

not attested not anchored not stored refs pending

Milnor Invariants and Twisted Whitney Towers

James Conant, Peter Teichner, Rob Schneiderman

arxiv:1102.0758 v5 · 2011-02-03 · 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{J7BE7URRK7OVDOBPTGF7OX7AOG}

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	2026-05-18T02:22:40.786820Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4fc24fd23157dd51b82f998bf75fe071afb94f6f3ca25f649908718117a454db

Aliases

arxiv: 1102.0758 · arxiv_version: 1102.0758v5 · doi: 10.48550/arxiv.1102.0758 · pith_short_12: J7BE7URRK7OV · pith_short_16: J7BE7URRK7OVDOBP · pith_short_8: J7BE7URR

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/J7BE7URRK7OVDOBPTGF7OX7AOG \
  | 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: 4fc24fd23157dd51b82f998bf75fe071afb94f6f3ca25f649908718117a454db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "25384b887e7637baa08d85b7cc46c308dd7f1b51845116e7d82b45e4b424453c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-02-03T19:51:33Z",
    "title_canon_sha256": "c3877dd787390bcc1fc22789e73b7f512e803449e687976f736c6f4d5927159d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.0758",
    "kind": "arxiv",
    "version": 5
  }
}