Pith Number

pith:K3NUK6OZ

pith:1997:K3NUK6OZLIEZNQ6EF3NSDSCQVF

not attested not anchored not stored refs pending

An invariant of smooth 4-manifolds

Laurence R. Taylor

arxiv:math/9712292 v1 · 1997-12-06 · 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{K3NUK6OZLIEZNQ6EF3NSDSCQVF}

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	2026-05-18T02:37:59.335321Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

56db4579d95a0996c3c42edb21c850a959b9cedd322983452007683c6c55c87b

Aliases

arxiv: math/9712292 · arxiv_version: math/9712292v1 · doi: 10.48550/arxiv.math/9712292 · pith_short_12: K3NUK6OZLIEZ · pith_short_16: K3NUK6OZLIEZNQ6E · pith_short_8: K3NUK6OZ

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/K3NUK6OZLIEZNQ6EF3NSDSCQVF \
  | 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: 56db4579d95a0996c3c42edb21c850a959b9cedd322983452007683c6c55c87b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d23719c17f5f1b632410f3de0cb0025b5890ee395e6f67f9bc58ce4e422cd6c",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1997-12-06T00:00:00Z",
    "title_canon_sha256": "519429bbb70b28f5548c6c90b0f9a50c9ff91a7250455192af76709baa7c1864"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9712292",
    "kind": "arxiv",
    "version": 1
  }
}