Pith Number

pith:HIQPV57O

pith:2023:HIQPV57OCJMFUL5BPL3PI4O6TS

not attested not anchored not stored refs pending

Exact results for some extremal problems on expansions I

Jialei Song, Long-tu Yuan, Xizhi Liu

arxiv:2310.01736 v2 · 2023-10-03 · 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{HIQPV57OCJMFUL5BPL3PI4O6TS}

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	2026-07-05T09:26:56.589497Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a20faf7ee12585a2fa17af6f471de9cb8e9d85e177ce0a2041a2b6ff123f207

Aliases

arxiv: 2310.01736 · arxiv_version: 2310.01736v2 · doi: 10.48550/arxiv.2310.01736 · pith_short_12: HIQPV57OCJMF · pith_short_16: HIQPV57OCJMFUL5B · pith_short_8: HIQPV57O

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/HIQPV57OCJMFUL5BPL3PI4O6TS \
  | 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: 3a20faf7ee12585a2fa17af6f471de9cb8e9d85e177ce0a2041a2b6ff123f207

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "15d90587882934136d08c0c346b42a87f80abe74a35ba5cd0002d5fbd0b8ab6a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-10-03T01:52:06Z",
    "title_canon_sha256": "78457410b2802bdae38e4f71f54132d030b816cd57ed38966f9a2fffacbf462d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2310.01736",
    "kind": "arxiv",
    "version": 2
  }
}