Pith Number

pith:WFZDP4MN

pith:2009:WFZDP4MNUYZY5JHNJ6PB4FN4WG

not attested not anchored not stored refs pending

The systolic constant of orientable Bieberbach 3-manifolds

Chady Elmir, Jacques Lafontaine

arxiv:0912.3894 v2 · 2009-12-19 · 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{WFZDP4MNUYZY5JHNJ6PB4FN4WG}

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	2026-05-18T02:57:00.310793Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b17237f18da6338ea4ed4f9e1e15bcb1a81de807981921a62f854980c0dfea14

Aliases

arxiv: 0912.3894 · arxiv_version: 0912.3894v2 · doi: 10.48550/arxiv.0912.3894 · pith_short_12: WFZDP4MNUYZY · pith_short_16: WFZDP4MNUYZY5JHN · pith_short_8: WFZDP4MN

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/WFZDP4MNUYZY5JHNJ6PB4FN4WG \
  | 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: b17237f18da6338ea4ed4f9e1e15bcb1a81de807981921a62f854980c0dfea14

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "881535679e632492b0eb2fe388fb7a7a1dbee84223ec0f8eea800d6fcaa13454",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-12-19T13:22:55Z",
    "title_canon_sha256": "d90bc17206264a215ba94d9a0ea1c510811a8842e7c0dd2ee4c5020d4e91b62f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.3894",
    "kind": "arxiv",
    "version": 2
  }
}