Pith Number

pith:MPTZYBGB

pith:2014:MPTZYBGB3XB4OOEJFYDCBXEGJ6

not attested not anchored not stored refs pending

Lagrangian Cobordisms via Generating Families: Constructions and Geography

Frederic Bourgeois, Joshua M. Sabloff, Lisa Traynor

arxiv:1409.3152 v2 · 2014-09-10 · 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{MPTZYBGB3XB4OOEJFYDCBXEGJ6}

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	2026-05-18T01:31:46.465598Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63e79c04c1ddc3c738892e0620dc864f857eb336cdd814f0327299d2e6a8e470

Aliases

arxiv: 1409.3152 · arxiv_version: 1409.3152v2 · doi: 10.48550/arxiv.1409.3152 · pith_short_12: MPTZYBGB3XB4 · pith_short_16: MPTZYBGB3XB4OOEJ · pith_short_8: MPTZYBGB

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/MPTZYBGB3XB4OOEJFYDCBXEGJ6 \
  | 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: 63e79c04c1ddc3c738892e0620dc864f857eb336cdd814f0327299d2e6a8e470

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "67810e01045552da14160d0384280791ac2ae8ac95822507d47281b800e14e86",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2014-09-10T16:56:10Z",
    "title_canon_sha256": "b9f4320aeaa70dcf19c92d74c1253fae78639f70771c08f06dd4586ce42fdc29"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.3152",
    "kind": "arxiv",
    "version": 2
  }
}