Pith Number

pith:XN4I2SA4

pith:2026:XN4I2SA4QPS66N6Z2ITFFIQKPE

not attested not anchored not stored refs pending

Supersaturation of induced even cycles in locally sparse graphs

Adam D\v{z}avoronok, Alexander Mylet, Maria-Cristina Popa, Ole Gabsdil, Yinghan Andie Shao

arxiv:2608.04985 v1 · 2026-08-05 · 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{XN4I2SA4QPS66N6Z2ITFFIQKPE}

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	2026-08-06T01:47:59.900398Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb788d481c83e5ef37d9d22652a20a79129ee091e5eafd58e474d0c406d2863a

Aliases

arxiv: 2608.04985 · arxiv_version: 2608.04985v1 · doi: 10.48550/arxiv.2608.04985 · pith_short_12: XN4I2SA4QPS6 · pith_short_16: XN4I2SA4QPS66N6Z · pith_short_8: XN4I2SA4

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/XN4I2SA4QPS66N6Z2ITFFIQKPE \
  | 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: bb788d481c83e5ef37d9d22652a20a79129ee091e5eafd58e474d0c406d2863a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5badd655a73b6acd9d291107a102db61d173ccf64f8379dbaa048727c609214b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-08-05T15:57:19Z",
    "title_canon_sha256": "b3f4ea0cc39bda1354c4e40787f21407143b5a6a1e99ea3166fd50bbac587328"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.04985",
    "kind": "arxiv",
    "version": 1
  }
}