Pith Number

pith:SZ3I654R

pith:2016:SZ3I654RCBPTYITO2LQXEQGAUI

not attested not anchored not stored refs pending

Some properties of optimal functions for sphere packing in dimensions 8 and 24

Henry Cohn, Stephen D. Miller

arxiv:1603.04759 v1 · 2016-03-15 · 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{SZ3I654RCBPTYITO2LQXEQGAUI}

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	2026-05-18T01:19:04.025547Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

96768f7791105f3c226ed2e17240c0a2035cdae490b505d8fa374e847d417498

Aliases

arxiv: 1603.04759 · arxiv_version: 1603.04759v1 · doi: 10.48550/arxiv.1603.04759 · pith_short_12: SZ3I654RCBPT · pith_short_16: SZ3I654RCBPTYITO · pith_short_8: SZ3I654R

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/SZ3I654RCBPTYITO2LQXEQGAUI \
  | 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: 96768f7791105f3c226ed2e17240c0a2035cdae490b505d8fa374e847d417498

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9890b5413a6d2242044a7dbde0cc7902e00df45a031f9dd348f97d4788a03bbb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2016-03-15T16:53:12Z",
    "title_canon_sha256": "2bb40fa77f19a01ff61a95a881f2bf1c802d805550ea6ce5fb291cfa22a41514"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.04759",
    "kind": "arxiv",
    "version": 1
  }
}