Pith Number

pith:X3HZEKDE

pith:2009:X3HZEKDEAZMNDGOCGPEPDKPYKQ

not attested not anchored not stored refs pending

Geometric inflexibility and 3-manifolds that fiber over the circle

Jeffrey Brock, Kenneth Bromberg

arxiv:0901.3870 v2 · 2009-01-25 · math.GT · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X3HZEKDEAZMNDGOCGPEPDKPYKQ}

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	2026-05-18T02:31:18.379046Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

becf9228640658d199c233c8f1a9f8543bb47580816c0bd57aa1fa68e61a4e5b

Aliases

arxiv: 0901.3870 · arxiv_version: 0901.3870v2 · doi: 10.48550/arxiv.0901.3870 · pith_short_12: X3HZEKDEAZMN · pith_short_16: X3HZEKDEAZMNDGOC · pith_short_8: X3HZEKDE

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/X3HZEKDEAZMNDGOCGPEPDKPYKQ \
  | 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: becf9228640658d199c233c8f1a9f8543bb47580816c0bd57aa1fa68e61a4e5b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8dcbafc6b939a9dd9fbd75bb166df44c976f42a0595afbbf185e00a2ff8ac0d",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-01-25T02:28:46Z",
    "title_canon_sha256": "bd9862caebd3859edae1b52759c926d9eed8649722352e7a5d9f328e623612ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0901.3870",
    "kind": "arxiv",
    "version": 2
  }
}