Pith Number

pith:AMW2GQHX

pith:2026:AMW2GQHXUBTMYL4TJFGDDCWXZH

not attested not anchored not stored refs pending

Structural Reductions for Monochromatic Matchings and Ramsey Tilings

Hong Liu, Lanchao Wang, Maksim Turevskii, Zhifei Yan

arxiv:2606.24863 v1 · 2026-06-23 · 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{AMW2GQHXUBTMYL4TJFGDDCWXZH}

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	2026-06-24T01:15:44.853597Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

032da340f7a066cc2f93494c318ad7c9e972de32e33367add7d273aec91594f4

Aliases

arxiv: 2606.24863 · arxiv_version: 2606.24863v1 · doi: 10.48550/arxiv.2606.24863 · pith_short_12: AMW2GQHXUBTM · pith_short_16: AMW2GQHXUBTMYL4T · pith_short_8: AMW2GQHX

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/AMW2GQHXUBTMYL4TJFGDDCWXZH \
  | 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: 032da340f7a066cc2f93494c318ad7c9e972de32e33367add7d273aec91594f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "08bd465dec18df84b09882133a586cd42394683bc002299d1143560584828307",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-23T17:44:38Z",
    "title_canon_sha256": "6e44895e4a67a5f97eca7db590f4d149641bd2b421436e5c4dafefc4e0a1cadf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.24863",
    "kind": "arxiv",
    "version": 1
  }
}