Pith Number

pith:MOJR3ACL

pith:2001:MOJR3ACLXTLB2A5G4QCNDD3UXN

not attested not anchored not stored refs pending

New upper bounds on sphere packings I

Henry Cohn, Noam Elkies

arxiv:math/0110009 v3 · 2001-10-01 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MOJR3ACLXTLB2A5G4QCNDD3UXN}

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	2026-05-18T04:00:03.004171Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63931d804bbcd61d03a6e404d18f74bb607b05202c0a59a63f66f09792714e64

Aliases

arxiv: math/0110009 · arxiv_version: math/0110009v3 · doi: 10.48550/arxiv.math/0110009 · pith_short_12: MOJR3ACLXTLB · pith_short_16: MOJR3ACLXTLB2A5G · pith_short_8: MOJR3ACL

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/MOJR3ACLXTLB2A5G4QCNDD3UXN \
  | 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: 63931d804bbcd61d03a6e404d18f74bb607b05202c0a59a63f66f09792714e64

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6cba35f8908e467fbc7bf0afd9567ee851512b1ebfa9fd624118ad9c58351637",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.MG",
    "submitted_at": "2001-10-01T09:32:11Z",
    "title_canon_sha256": "d065efc5c9992e8b6161c77616338228586bf44cc572025471ddada04b0ff1eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0110009",
    "kind": "arxiv",
    "version": 3
  }
}