Pith Number

pith:CTHA536C

pith:2026:CTHA536C6CUFLXADSJZPVWWAV5

not attested not anchored not stored refs pending

On the spectrum and structure of blowup thresholds

Hong Liu, Mingyuan Rong, Xinqi Huang

arxiv:2607.03035 v1 · 2026-07-03 · 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{CTHA536C6CUFLXADSJZPVWWAV5}

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	2026-07-07T01:16:40.740037Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14ce0eefc2f0a855dc039272fadac0af55d9e7951157269883a852094db9f4a8

Aliases

arxiv: 2607.03035 · arxiv_version: 2607.03035v1 · doi: 10.48550/arxiv.2607.03035 · pith_short_12: CTHA536C6CUF · pith_short_16: CTHA536C6CUFLXAD · pith_short_8: CTHA536C

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/CTHA536C6CUFLXADSJZPVWWAV5 \
  | 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: 14ce0eefc2f0a855dc039272fadac0af55d9e7951157269883a852094db9f4a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4fa8bb57f04c284b029310a9ec1ad2d86414eb67ac34baddd25161fe07a70e8e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-03T07:28:38Z",
    "title_canon_sha256": "0391a5847c9075e0c78b8cc025a2304c370b26f1c4b8f71fe55cf0372b56de74"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.03035",
    "kind": "arxiv",
    "version": 1
  }
}