Pith Number

pith:ZMKMDC4X

pith:2004:ZMKMDC4XIO3KDX3SUJDZ7N4DRW

not attested not anchored not stored refs pending

Constructing symplectic forms on 4-manifolds which vanish on circles

David T. Gay, Robion Kirby

arxiv:math/0401186 v2 · 2004-01-15 · math.GT · math.DG · 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{ZMKMDC4XIO3KDX3SUJDZ7N4DRW}

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	2026-05-18T02:38:00.191253Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb14c18b9743b6a1df72a2479fb7838d95187cbf7e821e4eb09f34ffefd5231a

Aliases

arxiv: math/0401186 · arxiv_version: math/0401186v2 · doi: 10.48550/arxiv.math/0401186 · pith_short_12: ZMKMDC4XIO3K · pith_short_16: ZMKMDC4XIO3KDX3S · pith_short_8: ZMKMDC4X

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/ZMKMDC4XIO3KDX3SUJDZ7N4DRW \
  | 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: cb14c18b9743b6a1df72a2479fb7838d95187cbf7e821e4eb09f34ffefd5231a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8334f018906c47d20eb2a879c653d284acee592d62565442c688a3f7e485fbfa",
    "cross_cats_sorted": [
      "math.DG",
      "math.SG"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2004-01-15T17:25:34Z",
    "title_canon_sha256": "fd61e38bdde063d51a68e23249a65575848e8946329ce7c05813e74bb28b11c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0401186",
    "kind": "arxiv",
    "version": 2
  }
}