Pith Number

pith:TCGBKYSY

pith:2021:TCGBKYSYXKJQ2CYUTLOJON72PX

not attested not anchored not stored refs pending

Legendre pairs of lengths $\ell \equiv 0$ (mod $3$)

Christoph Koutschan, Ilias Kotsireas

arxiv:2101.03116 v3 · 2021-01-08 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TCGBKYSYXKJQ2CYUTLOJON72PX}

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	2026-07-05T03:23:06.971486Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

988c156258ba930d0b149adc9737fa7dff61ad14afd33a6969438df464d785d3

Aliases

arxiv: 2101.03116 · arxiv_version: 2101.03116v3 · doi: 10.48550/arxiv.2101.03116 · pith_short_12: TCGBKYSYXKJQ · pith_short_16: TCGBKYSYXKJQ2CYU · pith_short_8: TCGBKYSY

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/TCGBKYSYXKJQ2CYUTLOJON72PX \
  | 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: 988c156258ba930d0b149adc9737fa7dff61ad14afd33a6969438df464d785d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e6d447f26d49052a32e2994d531776021be6b21312043325425e07af65e5002",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-01-08T17:16:05Z",
    "title_canon_sha256": "891503a5118475488793acc4bc1af5eca09b84325f4878f0c0cbdcf0cfd722a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2101.03116",
    "kind": "arxiv",
    "version": 3
  }
}