Pith Number

pith:UFR6EDZJ

pith:2010:UFR6EDZJOBUXIPIYC7L4HWA5RS

not attested not anchored not stored refs pending

Minimal immersions of closed surfaces in hyperbolic three-manifolds

Marcello Lucia, Zheng Huang

arxiv:1011.1313 v1 · 2010-11-05 · math.DG · math.AP · 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{UFR6EDZJOBUXIPIYC7L4HWA5RS}

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	2026-05-18T03:26:00.432530Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a163e20f297069743d1817d7c3d81d8c883773ba35898126da74bab364d53a9f

Aliases

arxiv: 1011.1313 · arxiv_version: 1011.1313v1 · doi: 10.48550/arxiv.1011.1313 · pith_short_12: UFR6EDZJOBUX · pith_short_16: UFR6EDZJOBUXIPIY · pith_short_8: UFR6EDZJ

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/UFR6EDZJOBUXIPIYC7L4HWA5RS \
  | 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: a163e20f297069743d1817d7c3d81d8c883773ba35898126da74bab364d53a9f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "65d923884959a9db07d0b3d45218c9dff5c42f9fc2c6f5ab8c7cdca7631e5596",
    "cross_cats_sorted": [
      "math.AP",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-11-05T02:41:01Z",
    "title_canon_sha256": "fc2dd42959b1551955e819359e99200a415dd3a31ab365efa2a145ef305221f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.1313",
    "kind": "arxiv",
    "version": 1
  }
}