Pith Number

pith:IYINRBND

pith:2017:IYINRBNDHSNT32OBPDLRMYAASQ

not attested not anchored not stored refs pending

Geometry and Arithmetic of Crystallographic Sphere Packings

Alex Kontorovich, Kei Nakamura

arxiv:1712.00147 v1 · 2017-12-01 · math.MG · math.GT · 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{IYINRBNDHSNT32OBPDLRMYAASQ}

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	2026-05-18T00:29:07.175209Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4610d885a33c9b3de9c178d71660009420d6bb277852e2eee98490be6cd79c4b

Aliases

arxiv: 1712.00147 · arxiv_version: 1712.00147v1 · doi: 10.48550/arxiv.1712.00147 · pith_short_12: IYINRBNDHSNT · pith_short_16: IYINRBNDHSNT32OB · pith_short_8: IYINRBND

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/IYINRBNDHSNT32OBPDLRMYAASQ \
  | 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: 4610d885a33c9b3de9c178d71660009420d6bb277852e2eee98490be6cd79c4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f6b841d46e2cf7f50e8f8140995aae8ea195eaf40b7fb1129139cb96f7e5ff3",
    "cross_cats_sorted": [
      "math.GT",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2017-12-01T01:40:28Z",
    "title_canon_sha256": "2b8d84b4d46ae1e4d9e717b933dc5b6b22b4490bc9784c534c7e0324798d8e5b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.00147",
    "kind": "arxiv",
    "version": 1
  }
}