Pith Number

pith:VGQWZ65U

pith:2006:VGQWZ65UDZNVNCEVEYPIGF3MFF

not attested not anchored not stored refs pending

Systoles of hyperbolic 4-manifolds

Ian Agol

arxiv:math/0612290 v1 · 2006-12-11 · 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{VGQWZ65UDZNVNCEVEYPIGF3MFF}

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

3 papers in Pith

Systole, inradius and rigidity of cusped hyperbolic 3-manifolds

On Systole, Kissing Number and Volume of Arithmetic Manifolds

Stably tangential strict hyperbolization

Receipt and verification

First computed	2026-07-04T14:49:36.039473Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9a16cfbb41e5b568895261e83176c2973da3edfc666628c6443186f1d83938e

Aliases

arxiv: math/0612290 · arxiv_version: math/0612290v1 · doi: 10.48550/arxiv.math/0612290 · pith_short_12: VGQWZ65UDZNV · pith_short_16: VGQWZ65UDZNVNCEV · pith_short_8: VGQWZ65U

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/VGQWZ65UDZNVNCEVEYPIGF3MFF \
  | 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: a9a16cfbb41e5b568895261e83176c2973da3edfc666628c6443186f1d83938e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1eb93e0888c8b80f2b1ac6b233f473919788e9534b34616e9c47989c39684f41",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2006-12-11T22:49:31Z",
    "title_canon_sha256": "90e66964a0790fa739d5fbd852dd93b6015f07f63bdec6ac31fc7c38d1c074c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0612290",
    "kind": "arxiv",
    "version": 1
  }
}