Pith Number

pith:KCSL4SOL

pith:2015:KCSL4SOLPM2LX6SDAOTNOYZBEC

not attested not anchored not stored refs pending

Energy bounds for codes and designs in Hamming spaces

Douglas P. Hardin, Edward B. Saff, Maya M. Stoyanova, Peter D. Dragnev, Peter G. Boyvalenkov

arxiv:1510.03406 v2 · 2015-10-12 · 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{KCSL4SOLPM2LX6SDAOTNOYZBEC}

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	2026-05-18T01:02:13.607425Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50a4be49cb7b34bbfa4303a6d7632120be60ff66cd8add371ac7e8585f9f568f

Aliases

arxiv: 1510.03406 · arxiv_version: 1510.03406v2 · doi: 10.48550/arxiv.1510.03406 · pith_short_12: KCSL4SOLPM2L · pith_short_16: KCSL4SOLPM2LX6SD · pith_short_8: KCSL4SOL

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/KCSL4SOLPM2LX6SDAOTNOYZBEC \
  | 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: 50a4be49cb7b34bbfa4303a6d7632120be60ff66cd8add371ac7e8585f9f568f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ada7fa5cf0387d0508cc1c095de58fe79d53cedf993d6b13d3baff1ff6484359",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2015-10-12T19:38:28Z",
    "title_canon_sha256": "fe1aea776bdf1a010c7373eeafdea5dd5b2ff510357ff8630f7e967b93519e00"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.03406",
    "kind": "arxiv",
    "version": 2
  }
}