Pith Number

pith:YKL2GF5G

pith:1996:YKL2GF5GV722HR264QYHHJEBWQ

not attested not anchored not stored refs pending

Circle-valued Morse theory, Reidemeister torsion, and Seiberg-Witten invariants of 3-manifolds

Michael Hutchings, Yi-Jen Lee

arxiv:dg-ga/9612004 v1 · 1996-12-03 · dg-ga · 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{YKL2GF5GV722HR264QYHHJEBWQ}

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	2026-05-18T01:06:48.548256Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c297a317a6aff5a3c75ee43073a481b40d1ede6e222432f958db1e0a783a8e80

Aliases

arxiv: dg-ga/9612004 · arxiv_version: dg-ga/9612004v1 · doi: 10.48550/arxiv.dg-ga/9612004 · pith_short_12: YKL2GF5GV722 · pith_short_16: YKL2GF5GV722HR26 · pith_short_8: YKL2GF5G

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/YKL2GF5GV722HR264QYHHJEBWQ \
  | 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: c297a317a6aff5a3c75ee43073a481b40d1ede6e222432f958db1e0a783a8e80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4a41d2fb9368de995ca64a672aeac2432bac3e683f573322c779b029a756578",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "",
    "primary_cat": "dg-ga",
    "submitted_at": "1996-12-03T17:58:11Z",
    "title_canon_sha256": "151cf67d9a4a4090664001cc7356d43be491f6a8f87a7fcf4921fa8693242809"
  },
  "schema_version": "1.0",
  "source": {
    "id": "dg-ga/9612004",
    "kind": "arxiv",
    "version": 1
  }
}