Pith Number

pith:56UZSAAF

pith:1999:56UZSAAFE3TMGE5GGKRL4NKLWD

not attested not anchored not stored refs pending

Reidemeister torsion in generalized Morse theory

Michael Hutchings

arxiv:math/9907066 v2 · 1999-07-12 · math.DG · math.DS · math.SG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{56UZSAAFE3TMGE5GGKRL4NKLWD}

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	2026-07-04T14:41:14.009176Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efa999000526e6c313a632a2be354bb0d91a1588ab0e8b4b193a59ebff38483f

Aliases

arxiv: math/9907066 · arxiv_version: math/9907066v2 · doi: 10.48550/arxiv.math/9907066 · pith_short_12: 56UZSAAFE3TM · pith_short_16: 56UZSAAFE3TMGE5G · pith_short_8: 56UZSAAF

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/56UZSAAFE3TMGE5GGKRL4NKLWD \
  | 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: efa999000526e6c313a632a2be354bb0d91a1588ab0e8b4b193a59ebff38483f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f63aa123a56f2df042c91cbaa51e693976c036d638fd3cc3048ffbefdec0c86",
    "cross_cats_sorted": [
      "math.DS",
      "math.SG"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "1999-07-12T20:01:07Z",
    "title_canon_sha256": "7509239322be4045c811e0f099ed6bb287d55126ddcf39b3d9f342eadcf6f60f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9907066",
    "kind": "arxiv",
    "version": 2
  }
}