Pith Number

pith:X7SID7CB

pith:2025:X7SID7CBSUEM2SRZND7S3GRTJ7

not attested not anchored not stored refs pending

Universal optimality of $T$-avoiding spherical codes and designs

D. D. Cherkashin, P. D. Dragnev, P. G. Boyvalenkov

arxiv:2501.13906 v2 · 2025-01-23 · math.CO · cs.IT · math.IT · 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{X7SID7CBSUEM2SRZND7S3GRTJ7}

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	2026-05-20T00:02:48.142250Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfe481fc419508cd4a3968ff2d9a334ff6df7a474ca3b1ad518a7ae15c29794d

Aliases

arxiv: 2501.13906 · arxiv_version: 2501.13906v2 · doi: 10.48550/arxiv.2501.13906 · pith_short_12: X7SID7CBSUEM · pith_short_16: X7SID7CBSUEM2SRZ · pith_short_8: X7SID7CB

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/X7SID7CBSUEM2SRZND7S3GRTJ7 \
  | 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: bfe481fc419508cd4a3968ff2d9a334ff6df7a474ca3b1ad518a7ae15c29794d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a7abcbd62bfb4845e36b3dfb81bec6bec50f9c72437b805c46088f15e032280",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-01-23T18:36:51Z",
    "title_canon_sha256": "536051f97c97f4cf24fb48b83b2b500c7c707a6d1e04ed93ebeeebb2fb492206"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.13906",
    "kind": "arxiv",
    "version": 2
  }
}