Pith Number

pith:TTJT425C

pith:2026:TTJT425C7UZFYP5IYMWC6HPI5O

not attested not anchored not stored refs pending

Linear equations and chromatic thresholds in $B_h$ sets

Nathan Tung

arxiv:2606.30767 v1 · 2026-06-29 · math.CO · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TTJT425C7UZFYP5IYMWC6HPI5O}

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	2026-07-01T00:17:16.413002Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9cd33e6ba2fd325c3fa8c32c2f1de8eb8dbf2d90252d05390c70032dec3ec51a

Aliases

arxiv: 2606.30767 · arxiv_version: 2606.30767v1 · doi: 10.48550/arxiv.2606.30767 · pith_short_12: TTJT425C7UZF · pith_short_16: TTJT425C7UZFYP5I · pith_short_8: TTJT425C

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/TTJT425C7UZFYP5IYMWC6HPI5O \
  | 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: 9cd33e6ba2fd325c3fa8c32c2f1de8eb8dbf2d90252d05390c70032dec3ec51a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ea318c3198690aaec5d2e5821e503ead0c1ec2ddb1414d86e12d45825e5ae8d",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-29T18:02:41Z",
    "title_canon_sha256": "ab444dd4b14ae377fcb00e7da3363cc15433be5845fd176db61dfe61504e55e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.30767",
    "kind": "arxiv",
    "version": 1
  }
}