Pith Number

pith:LYLHU4S7

pith:2014:LYLHU4S7VLNUETRPEHCSXOIVVK

not attested not anchored not stored refs pending

Ranks of mapping tori via the curve complex

Ian Biringer, Juan Souto

arxiv:1409.1878 v2 · 2014-09-05 · 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{LYLHU4S7VLNUETRPEHCSXOIVVK}

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	2026-05-18T00:39:48.325469Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e167a725faadb424e2f21c52bb915aab25ca90ba5a60d69d862ae5d2a003c9c

Aliases

arxiv: 1409.1878 · arxiv_version: 1409.1878v2 · doi: 10.48550/arxiv.1409.1878 · pith_short_12: LYLHU4S7VLNU · pith_short_16: LYLHU4S7VLNUETRP · pith_short_8: LYLHU4S7

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/LYLHU4S7VLNUETRPEHCSXOIVVK \
  | 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: 5e167a725faadb424e2f21c52bb915aab25ca90ba5a60d69d862ae5d2a003c9c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2452921912cb3bf4b11b966848ed6d36e746bec0e6301e7a7bc53fe5fcc9e437",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2014-09-05T17:17:15Z",
    "title_canon_sha256": "449e6fa909b707e3898e1ced5b354ddf2ef894173af7d1c5b74bbb2f472ababa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.1878",
    "kind": "arxiv",
    "version": 2
  }
}