Pith Number

pith:I6J3IL2T

pith:2013:I6J3IL2T6NSMZXTI2VKED5BZSW

not attested not anchored not stored refs pending

Families of Legendrian Submanifolds via Generating Families

Joshua M. Sabloff, Michael G. Sullivan

arxiv:1311.0528 v1 · 2013-11-03 · 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{I6J3IL2T6NSMZXTI2VKED5BZSW}

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	2026-05-18T03:08:05.617557Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4793b42f53f364ccde68d55441f43995aad6588370a3db10fa6787db3c087f29

Aliases

arxiv: 1311.0528 · arxiv_version: 1311.0528v1 · doi: 10.48550/arxiv.1311.0528 · pith_short_12: I6J3IL2T6NSM · pith_short_16: I6J3IL2T6NSMZXTI · pith_short_8: I6J3IL2T

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/I6J3IL2T6NSMZXTI2VKED5BZSW \
  | 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: 4793b42f53f364ccde68d55441f43995aad6588370a3db10fa6787db3c087f29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9de40fbf0a14f1cd3608f567ee093eca46a75658a0f7b439d888dbc5354462f",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2013-11-03T21:04:53Z",
    "title_canon_sha256": "6df32beb6d458f07147d900ad467710cd328494fa39f126f9880bd653a82b09e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.0528",
    "kind": "arxiv",
    "version": 1
  }
}