Pith Number

pith:QYJ57ZIV

pith:2015:QYJ57ZIVAYLLRZ7TTIQ3JSVHDB

not attested not anchored not stored refs pending

Maximal Thurston-Bennequin number and reducible Legendrian surgery

Kouichi Yasui

arxiv:1508.05615 v3 · 2015-08-23 · math.GT · 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{QYJ57ZIVAYLLRZ7TTIQ3JSVHDB}

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	2026-05-17T23:53:13.648616Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8613dfe5150616b8e7f39a21b4caa7186a220f641997fd8c41879f2aeb76dae2

Aliases

arxiv: 1508.05615 · arxiv_version: 1508.05615v3 · doi: 10.48550/arxiv.1508.05615 · pith_short_12: QYJ57ZIVAYLL · pith_short_16: QYJ57ZIVAYLLRZ7T · pith_short_8: QYJ57ZIV

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/QYJ57ZIVAYLLRZ7TTIQ3JSVHDB \
  | 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: 8613dfe5150616b8e7f39a21b4caa7186a220f641997fd8c41879f2aeb76dae2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a853150bc6d29ab5921f90c1ba72681af71ffc978e302072ab5dba282e938e37",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-08-23T14:57:34Z",
    "title_canon_sha256": "14a312ceafed7bf3a04d61c6d0aecfbbfd135d1be159f522843afc13af09f603"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.05615",
    "kind": "arxiv",
    "version": 3
  }
}