Pith Number

pith:N4AI7SY5

pith:2015:N4AI7SY5QHUZQ4T6UGNIP2NUNF

not attested not anchored not stored refs pending

Complex length of short curves and Minimal Fibration in hyperbolic $3$-Manifolds fibering over the circle

Biao Wang, Zheng Huang

arxiv:1512.03858 v4 · 2015-12-12 · math.DG · 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{N4AI7SY5QHUZQ4T6UGNIP2NUNF}

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	2026-05-17T23:59:44.059640Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f008fcb1d81e998727ea19a87e9b469795229d6de179c36772a8fbe98ee2f7d

Aliases

arxiv: 1512.03858 · arxiv_version: 1512.03858v4 · doi: 10.48550/arxiv.1512.03858 · pith_short_12: N4AI7SY5QHUZ · pith_short_16: N4AI7SY5QHUZQ4T6 · pith_short_8: N4AI7SY5

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/N4AI7SY5QHUZQ4T6UGNIP2NUNF \
  | 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: 6f008fcb1d81e998727ea19a87e9b469795229d6de179c36772a8fbe98ee2f7d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "109eef5c2016b94e06e6797142ca19c0a5c3d930b7138f192af5b3d383c9d5b4",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-12-12T01:52:49Z",
    "title_canon_sha256": "f876f09138fb1d0d28ca14cffdf6fec6d34d6dfaae1843b55c650d660c8e8e41"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.03858",
    "kind": "arxiv",
    "version": 4
  }
}