Pith Number

pith:G7PCKH2M

pith:2019:G7PCKH2MBUN3PLYMNKZMO4U775

not attested not anchored not stored refs pending

On 3-manifolds that are boundaries of exotic 4-manifolds

Anubhav Mukherjee, Hyunki Min, John B. Etnyre

arxiv:1901.07964 v3 · 2019-01-23 · math.GT · 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{G7PCKH2MBUN3PLYMNKZMO4U775}

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	2026-07-05T03:33:01.525147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

37de251f4c0d1bb7af0c6ab2c7729fff4d7423b11630bf302e8f8b8adc020d8b

Aliases

arxiv: 1901.07964 · arxiv_version: 1901.07964v3 · doi: 10.48550/arxiv.1901.07964 · pith_short_12: G7PCKH2MBUN3 · pith_short_16: G7PCKH2MBUN3PLYM · pith_short_8: G7PCKH2M

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/G7PCKH2MBUN3PLYMNKZMO4U775 \
  | 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: 37de251f4c0d1bb7af0c6ab2c7729fff4d7423b11630bf302e8f8b8adc020d8b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6ae8c21a4ba14b63a5cf51fcad157320b9a3e39aaee431e4bf16d150b945c490",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2019-01-23T15:48:37Z",
    "title_canon_sha256": "c6fc8e7b71738546a7036a785edfd8ecbb418771f61fa93e8dbc6f5f5c986e2a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.07964",
    "kind": "arxiv",
    "version": 3
  }
}