Pith Number

pith:S6R2Z3IK

pith:2019:S6R2Z3IKLIIPZVICCVY2BCOXVJ

not attested not anchored not stored refs pending

Kissing numbers of closed hyperbolic manifolds

Bram Petri, Maxime Fortier Bourque

arxiv:1905.11083 v1 · 2019-05-27 · 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{S6R2Z3IKLIIPZVICCVY2BCOXVJ}

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	2026-05-17T23:45:02.980079Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

97a3aced0a5a10fcd5021571a089d7aa4d8c1a3f19578210a3472aeddbe529d2

Aliases

arxiv: 1905.11083 · arxiv_version: 1905.11083v1 · doi: 10.48550/arxiv.1905.11083 · pith_short_12: S6R2Z3IKLIIP · pith_short_16: S6R2Z3IKLIIPZVIC · pith_short_8: S6R2Z3IK

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/S6R2Z3IKLIIPZVICCVY2BCOXVJ \
  | 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: 97a3aced0a5a10fcd5021571a089d7aa4d8c1a3f19578210a3472aeddbe529d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bcf2d723d3295290df8aad48aa3fa5224f3e5a0bd6b5d891ecec9c0614aa62b3",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2019-05-27T09:46:43Z",
    "title_canon_sha256": "ffefb31b009e1f334cd2d850cc9fc0dc4ae9d3d1178d69be750e456c8979075f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.11083",
    "kind": "arxiv",
    "version": 1
  }
}