Pith Number

pith:3VXN43AT

pith:2015:3VXN43ATBMVF7GZM5K2LIU42YQ

not attested not anchored not stored refs pending

Dehn twists exact sequences through Lagrangian cobordism

Cheuk Yu Mak, WeiWei Wu

arxiv:1509.08028 v2 · 2015-09-26 · math.SG · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3VXN43ATBMVF7GZM5K2LIU42YQ}

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	2026-05-17T23:53:13.591645Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd6ede6c130b2a5f9b2ceab4b4539ac42ea7187a95692c79e6239c3cf3ef7838

Aliases

arxiv: 1509.08028 · arxiv_version: 1509.08028v2 · doi: 10.48550/arxiv.1509.08028 · pith_short_12: 3VXN43ATBMVF · pith_short_16: 3VXN43ATBMVF7GZM · pith_short_8: 3VXN43AT

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/3VXN43ATBMVF7GZM5K2LIU42YQ \
  | 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: dd6ede6c130b2a5f9b2ceab4b4539ac42ea7187a95692c79e6239c3cf3ef7838

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9a7e51b1f3347cefbc770689b3b3d9b1b844d9bd0a987d4e3e4e98dce5f71ec",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2015-09-26T21:17:08Z",
    "title_canon_sha256": "5e8bf2c4e240d1072b9ca62ebedbba333b0e7a5ff9321c1b294ec9c18a9e6639"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.08028",
    "kind": "arxiv",
    "version": 2
  }
}