Pith Number

pith:LMWHOQWV

pith:2026:LMWHOQWVDIMW4JJOI2ZVQ7V4WG

not attested not anchored not stored refs pending

Tree-partitions of graphs with bounded tree-depth

Huayue Liu, Rong chen

arxiv:2608.12723 v1 · 2026-08-13 · 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{LMWHOQWVDIMW4JJOI2ZVQ7V4WG}

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	2026-08-14T00:47:08.932158Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5b2c7742d51a196e252e46b3587ebcb196808a0204ddf9fef085082fb4c8addc

Aliases

arxiv: 2608.12723 · arxiv_version: 2608.12723v1 · doi: 10.48550/arxiv.2608.12723 · pith_short_12: LMWHOQWVDIMW · pith_short_16: LMWHOQWVDIMW4JJO · pith_short_8: LMWHOQWV

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/LMWHOQWVDIMW4JJOI2ZVQ7V4WG \
  | 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: 5b2c7742d51a196e252e46b3587ebcb196808a0204ddf9fef085082fb4c8addc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b601c189b67242372a0460a680f9a6bc3e0089f7b3ffdcc100c2ba08ce6e287f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-08-13T02:09:50Z",
    "title_canon_sha256": "b1e1ad7c792ac3553a4e7d1ef163742fee917dcabbf7361e63d2eecbe2b30da2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.12723",
    "kind": "arxiv",
    "version": 1
  }
}