Pith Number

pith:7LD2XFJP

pith:2001:7LD2XFJPOHUEBMI5OE5QTJ5WH7

not attested not anchored not stored refs pending

Surgery formula for torsions and Seiberg-Witten invariants of 3-manifolds

Vladimir Turaev

arxiv:math/0101108 v1 · 2001-01-12 · 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{7LD2XFJPOHUEBMI5OE5QTJ5WH7}

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	2026-05-18T01:05:37.985458Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fac7ab952f71e840b11d713b09a7b63fd695840d34ff201ddccff1bf48dcec4b

Aliases

arxiv: math/0101108 · arxiv_version: math/0101108v1 · doi: 10.48550/arxiv.math/0101108 · pith_short_12: 7LD2XFJPOHUE · pith_short_16: 7LD2XFJPOHUEBMI5 · pith_short_8: 7LD2XFJP

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/7LD2XFJPOHUEBMI5OE5QTJ5WH7 \
  | 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: fac7ab952f71e840b11d713b09a7b63fd695840d34ff201ddccff1bf48dcec4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7968b4a4a0e67afeadf8844b1eb42df09ff6556008ff846c66e3140c08fd020d",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2001-01-12T15:34:39Z",
    "title_canon_sha256": "11df0d918911144a34e5e6fc5225495b85c58aec79121a83fb8d5dddcb7e1c0c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0101108",
    "kind": "arxiv",
    "version": 1
  }
}