Pith Number

pith:7PMX63BN

pith:2016:7PMX63BNRC7OELVEYHN2EOOETW

not attested not anchored not stored refs pending

An energy-capacity inequality for Legendrian submanifolds

Georgios Dimitroglou Rizell, Michael G. Sullivan

arxiv:1608.06232 v4 · 2016-08-22 · 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{7PMX63BNRC7OELVEYHN2EOOETW}

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	2026-05-18T00:07:18.978280Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fbd97f6c2d88bee22ea4c1dba239c49d867ab9ec7648280cd04303a68c0ce3a0

Aliases

arxiv: 1608.06232 · arxiv_version: 1608.06232v4 · doi: 10.48550/arxiv.1608.06232 · pith_short_12: 7PMX63BNRC7O · pith_short_16: 7PMX63BNRC7OELVE · pith_short_8: 7PMX63BN

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/7PMX63BNRC7OELVEYHN2EOOETW \
  | 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: fbd97f6c2d88bee22ea4c1dba239c49d867ab9ec7648280cd04303a68c0ce3a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "115220cf9ef714815e9075c5ac9171e8997213fbf1562a5bfa1c22315ce770f3",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2016-08-22T17:32:05Z",
    "title_canon_sha256": "eef7f2f2041e2fa8476d78c0a543d355cf47d28554864102f8572c82bb0da0fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.06232",
    "kind": "arxiv",
    "version": 4
  }
}