Pith Number

pith:F5J7GF7T

pith:1999:F5J7GF7TSEUOGS22HGRA6XPOMI

not attested not anchored not stored refs pending

Lower bounds on volumes of hyperbolic Haken 3-manifolds

Ian Agol

arxiv:math/9906182 v1 · 1999-06-27 · 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{F5J7GF7TSEUOGS22HGRA6XPOMI}

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.

Cited by

1 paper in Pith

Neoplatonic solids

Receipt and verification

First computed	2026-07-04T14:41:12.621139Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f53f317f39128e34b5a39a20f5dee6234b0344f856a33ee97022076af8cda39

Aliases

arxiv: math/9906182 · arxiv_version: math/9906182v1 · doi: 10.48550/arxiv.math/9906182 · pith_short_12: F5J7GF7TSEUO · pith_short_16: F5J7GF7TSEUOGS22 · pith_short_8: F5J7GF7T

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/F5J7GF7TSEUOGS22HGRA6XPOMI \
  | 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: 2f53f317f39128e34b5a39a20f5dee6234b0344f856a33ee97022076af8cda39

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee5b1ae6308401672764456f41994cf5642223dc2eebebeb93fdf727aaed46a9",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1999-06-27T03:42:16Z",
    "title_canon_sha256": "c4d13d5643fccb1604bc2368bdae127b6e3d2e52f6cf03853db89ec77243dd5a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9906182",
    "kind": "arxiv",
    "version": 1
  }
}