Pith Number

pith:ZJOMW5FJ

pith:2026:ZJOMW5FJZPQKNSIFZIHIPA4Q7R

not attested not anchored not stored refs pending

The continuous oriented chromatic number of directed Schreier graphs of \(\mathbb Z^2\)-shift actions

Ruijun Wang

arxiv:2607.00367 v1 · 2026-07-01 · math.LO · 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{ZJOMW5FJZPQKNSIFZIHIPA4Q7R}

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	2026-07-02T01:17:41.359359Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca5ccb74a9cbe0a6c905ca0e878390fc734d5d2ced72ac54ccc282ee1639189e

Aliases

arxiv: 2607.00367 · arxiv_version: 2607.00367v1 · doi: 10.48550/arxiv.2607.00367 · pith_short_12: ZJOMW5FJZPQK · pith_short_16: ZJOMW5FJZPQKNSIF · pith_short_8: ZJOMW5FJ

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/ZJOMW5FJZPQKNSIFZIHIPA4Q7R \
  | 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: ca5ccb74a9cbe0a6c905ca0e878390fc734d5d2ced72ac54ccc282ee1639189e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd7d10851d391ed490e5a4072827494f7fe01bc93a71206260f3e1dd95e6cdc4",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2026-07-01T03:05:25Z",
    "title_canon_sha256": "197b773007ba82c2bc002e0a7f73f6120a3bbbdff8faa9945b9aff4bd62a87e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.00367",
    "kind": "arxiv",
    "version": 1
  }
}