Pith Number

pith:6P3KRVMN

pith:2021:6P3KRVMNQHS25NIA3POAIHE5FQ

not attested not anchored not stored refs pending

On extremal numbers of the triangle plus the four-cycle

Jie Ma, Tianchi Yang

arxiv:2112.13689 v2 · 2021-12-27 · 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{6P3KRVMNQHS25NIA3POAIHE5FQ}

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	2026-07-05T05:22:05.601002Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3f6a8d58d81e5aeb500dbdc041c9d2c0f466e058680f271b9077cd9eb654cfd

Aliases

arxiv: 2112.13689 · arxiv_version: 2112.13689v2 · doi: 10.48550/arxiv.2112.13689 · pith_short_12: 6P3KRVMNQHS2 · pith_short_16: 6P3KRVMNQHS25NIA · pith_short_8: 6P3KRVMN

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/6P3KRVMNQHS25NIA3POAIHE5FQ \
  | 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: f3f6a8d58d81e5aeb500dbdc041c9d2c0f466e058680f271b9077cd9eb654cfd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95d8d1d5fc9d8cd748d971ee248fbb7fc68021a66ea401287a860e648503ade2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-12-27T13:57:05Z",
    "title_canon_sha256": "15afda1f8d63dda5be275f286c8ce404006ce4e375f73597f0a962300cdb5e3c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.13689",
    "kind": "arxiv",
    "version": 2
  }
}