Pith Number

pith:R4XD5XZ2

pith:2025:R4XD5XZ2EZ3MRU3ZXYCE6IMMIW

not attested not anchored not stored refs pending

On a conjecture of Pach-Spencer-T\'oth for graph crossing numbers

Jie Ma, Kaizhe Chen

arxiv:2502.02301 v1 · 2025-02-04 · 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{R4XD5XZ2EZ3MRU3ZXYCE6IMMIW}

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	2026-07-05T10:09:26.706728Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f2e3edf3a2676c8d379be044f218c45bcd16e6600c79b82c8d35f8055e62564

Aliases

arxiv: 2502.02301 · arxiv_version: 2502.02301v1 · doi: 10.48550/arxiv.2502.02301 · pith_short_12: R4XD5XZ2EZ3M · pith_short_16: R4XD5XZ2EZ3MRU3Z · pith_short_8: R4XD5XZ2

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/R4XD5XZ2EZ3MRU3ZXYCE6IMMIW \
  | 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: 8f2e3edf3a2676c8d379be044f218c45bcd16e6600c79b82c8d35f8055e62564

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c922cb6a627939d4b653bf3f08afe43ab4e7c8089dd2ad770f846c58a333580",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-02-04T13:15:17Z",
    "title_canon_sha256": "4be1563135f2aa9bb1b0cdd466046493e24961f3e8803b6a39403dc5b9c976ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.02301",
    "kind": "arxiv",
    "version": 1
  }
}