Pith Number

pith:PI2T6Q7V

pith:2009:PI2T6Q7V5V4JWLQ5G74PEW3L2Y

not attested not anchored not stored refs pending

Generalized fibre sums of 4-manifolds and the canonical class

M. J. D. Hamilton

arxiv:0907.2671 v4 · 2009-07-15 · math.SG · 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{PI2T6Q7V5V4JWLQ5G74PEW3L2Y}

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	2026-05-18T03:26:41.491119Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a353f43f5ed789b2e1d37f8f25b6bd622cd81c76fac95d277fc00593d861dab

Aliases

arxiv: 0907.2671 · arxiv_version: 0907.2671v4 · doi: 10.48550/arxiv.0907.2671 · pith_short_12: PI2T6Q7V5V4J · pith_short_16: PI2T6Q7V5V4JWLQ5 · pith_short_8: PI2T6Q7V

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/PI2T6Q7V5V4JWLQ5G74PEW3L2Y \
  | 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: 7a353f43f5ed789b2e1d37f8f25b6bd622cd81c76fac95d277fc00593d861dab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e6c969101869693c95ee886bc99b446e2b77121069ff57eb5f975a91dab195f",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2009-07-15T19:04:23Z",
    "title_canon_sha256": "b023b569cb5801e028222c09bed67a19872cfea8df4239121d52b9dc4d4ffafe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.2671",
    "kind": "arxiv",
    "version": 4
  }
}