Pith Number

pith:55KVTIZD

pith:2016:55KVTIZDN6KB7KOBPPXGSPPQJH

not attested not anchored not stored refs pending

On volumes of quasi-arithmetic hyperbolic lattices

Vincent Emery

arxiv:1603.07349 v3 · 2016-03-23 · math.MG · math.KT · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{55KVTIZDN6KB7KOBPPXGSPPQJH}

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	2026-05-18T00:22:49.440267Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef5559a3236f941fa9c17bee693df049fdb2320330c9450b2175d2f71f15dcf6

Aliases

arxiv: 1603.07349 · arxiv_version: 1603.07349v3 · doi: 10.48550/arxiv.1603.07349 · pith_short_12: 55KVTIZDN6KB · pith_short_16: 55KVTIZDN6KB7KOB · pith_short_8: 55KVTIZD

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/55KVTIZDN6KB7KOBPPXGSPPQJH \
  | 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: ef5559a3236f941fa9c17bee693df049fdb2320330c9450b2175d2f71f15dcf6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cdd6e26e47b056f33ddfbcffe10cf474d339c3761581ae51e9d750f2f664907b",
    "cross_cats_sorted": [
      "math.KT",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2016-03-23T20:34:44Z",
    "title_canon_sha256": "e5d5423cda6f352037d628dd23c7404420988e790f180710600c8988195cadca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.07349",
    "kind": "arxiv",
    "version": 3
  }
}