Pith Number

pith:QX5PQBSA

pith:2005:QX5PQBSAPNH5MVDAS65SGSS7HS

not attested not anchored not stored refs pending

The correspondence between augmentations and rulings for Legendrian knots

Joshua M. Sabloff, Lenhard L. Ng

arxiv:math/0503168 v2 · 2005-03-08 · 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{QX5PQBSAPNH5MVDAS65SGSS7HS}

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	2026-05-18T01:05:23.639615Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

85faf806407b4fd6546097bb234a5f3ca184fc79ff67b3d5726360bcefce97f6

Aliases

arxiv: math/0503168 · arxiv_version: math/0503168v2 · doi: 10.48550/arxiv.math/0503168 · pith_short_12: QX5PQBSAPNH5 · pith_short_16: QX5PQBSAPNH5MVDA · pith_short_8: QX5PQBSA

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/QX5PQBSAPNH5MVDAS65SGSS7HS \
  | 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: 85faf806407b4fd6546097bb234a5f3ca184fc79ff67b3d5726360bcefce97f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4bdf2f883b67935d0001c7e63670c81074c8bbb63453e1977846de6a17f66e49",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.SG",
    "submitted_at": "2005-03-08T22:59:35Z",
    "title_canon_sha256": "ce712c439861cfce7720ead280b76f1c0ff36dfca8464403f41ba1b3014d0738"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0503168",
    "kind": "arxiv",
    "version": 2
  }
}