Pith Number

pith:ZB4RIHZ2

pith:2013:ZB4RIHZ2DRFPXAF5OHU7LLKHXQ

not attested not anchored not stored refs pending

On compact hyperbolic manifolds of Euler characteristic two

Vincent Emery

arxiv:1304.3509 v2 · 2013-04-11 · 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{ZB4RIHZ2DRFPXAF5OHU7LLKHXQ}

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	2026-05-18T02:41:42.473148Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c879141f3a1c4afb80bd71e9f5ad47bc2314ecde7bbbe99f5ad44ae28f3b6e81

Aliases

arxiv: 1304.3509 · arxiv_version: 1304.3509v2 · doi: 10.48550/arxiv.1304.3509 · pith_short_12: ZB4RIHZ2DRFP · pith_short_16: ZB4RIHZ2DRFPXAF5 · pith_short_8: ZB4RIHZ2

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/ZB4RIHZ2DRFPXAF5OHU7LLKHXQ \
  | 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: c879141f3a1c4afb80bd71e9f5ad47bc2314ecde7bbbe99f5ad44ae28f3b6e81

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "30269967f647e2fa7f7f8a3339cd9cb219180568fe1f0ac8bacb587dfa058426",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-04-11T23:46:55Z",
    "title_canon_sha256": "1d6dd4d8c6d98f8064908bb197024dd4ccc4896f245146c775770646ec21543d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.3509",
    "kind": "arxiv",
    "version": 2
  }
}