Pith Number

pith:V2YOJZEH

pith:2021:V2YOJZEHEBUZJ73JA4ZEPGLP6Y

not attested not anchored not stored refs pending

Sphere packing bounds via rescaling

Andrew Salmon, Henry Cohn

arxiv:2108.10936 v1 · 2021-08-24 · 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{V2YOJZEHEBUZJ73JA4ZEPGLP6Y}

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	2026-07-05T03:08:47.650421Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aeb0e4e487206994ff69073247996ff61aabd0032c5d3c8edfaf9b8085e27119

Aliases

arxiv: 2108.10936 · arxiv_version: 2108.10936v1 · doi: 10.48550/arxiv.2108.10936 · pith_short_12: V2YOJZEHEBUZ · pith_short_16: V2YOJZEHEBUZJ73J · pith_short_8: V2YOJZEH

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/V2YOJZEHEBUZJ73JA4ZEPGLP6Y \
  | 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: aeb0e4e487206994ff69073247996ff61aabd0032c5d3c8edfaf9b8085e27119

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69443a7aa0645e14ac51cd037f064d01e94ae6eb8562329b77ed6449d72e9738",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2021-08-24T20:01:15Z",
    "title_canon_sha256": "591926e4b619a80cbc952b2c8ec1a9a9fd5d1adca4d89962edb361bedb69adfb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2108.10936",
    "kind": "arxiv",
    "version": 1
  }
}