Pith Number

pith:WTJSA6BE

pith:2026:WTJSA6BE7TZ5ZG5YIPH73ODMML

not attested not anchored not stored refs pending

An annihilation-number Caro-Wei bound: a TxGraffiti conjecture and an independence-number bracket

Chakshu Gupta

arxiv:2606.29553 v1 · 2026-06-28 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WTJSA6BE7TZ5ZG5YIPH73ODMML}

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	2026-06-30T01:18:11.735090Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b4d3207824fcf3dc9bb843cffdb86c62c40c02d0d683221df98dfa852e3fb045

Aliases

arxiv: 2606.29553 · arxiv_version: 2606.29553v1 · doi: 10.48550/arxiv.2606.29553 · pith_short_12: WTJSA6BE7TZ5 · pith_short_16: WTJSA6BE7TZ5ZG5Y · pith_short_8: WTJSA6BE

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/WTJSA6BE7TZ5ZG5YIPH73ODMML \
  | 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: b4d3207824fcf3dc9bb843cffdb86c62c40c02d0d683221df98dfa852e3fb045

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f907e9d16b7b19077ddcf159f03392130ce35ae9a215a3c6639134221184578",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-28T18:36:06Z",
    "title_canon_sha256": "08a2b5035838a1d5a2c969c391b5c78caa8f49d32c205a6b79a77bbb7c69c211"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.29553",
    "kind": "arxiv",
    "version": 1
  }
}