Pith Number

pith:J53QZDTK

pith:2015:J53QZDTKZ3UMPFLYIHMRHFW43J

not attested not anchored not stored refs pending

The cardinality of the augmentation category of a Legendrian link

Dan Rutherford, Lenhard Ng, Steven Sivek, Vivek Shende

arxiv:1511.06724 v1 · 2015-11-20 · 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{J53QZDTKZ3UMPFLYIHMRHFW43J}

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	2026-05-18T00:24:54.567016Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f770c8e6acee8c7957841d91396dcda711cea9ee7ea8ff6b782eb1b8f1d081c

Aliases

arxiv: 1511.06724 · arxiv_version: 1511.06724v1 · doi: 10.48550/arxiv.1511.06724 · pith_short_12: J53QZDTKZ3UM · pith_short_16: J53QZDTKZ3UMPFLY · pith_short_8: J53QZDTK

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/J53QZDTKZ3UMPFLYIHMRHFW43J \
  | 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: 4f770c8e6acee8c7957841d91396dcda711cea9ee7ea8ff6b782eb1b8f1d081c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef88e774552869c9a4f434694b18fe3ec29f47fe3f6a2eba8c2ddfe8d704ab77",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2015-11-20T18:56:24Z",
    "title_canon_sha256": "198f00c265efcadb35db41adb7e93238b625d7a6ff8b251fece17b8094475024"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.06724",
    "kind": "arxiv",
    "version": 1
  }
}