Pith Number

pith:GNHIISQP

pith:2026:GNHIISQPIXK7RQSCKLBALFG57X

not attested not anchored not stored refs pending

Pyramidal Width Can Increase Under Vertex Insertion

Jinze Zhao

arxiv:2607.29555 v1 · 2026-07-31 · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GNHIISQPIXK7RQSCKLBALFG57X}

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	2026-08-03T01:38:24.704821Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

334e844a0f45d5f8c24252c20594ddfdec51198cfe2ff3acabace22b916e190c

Aliases

arxiv: 2607.29555 · arxiv_version: 2607.29555v1 · doi: 10.48550/arxiv.2607.29555 · pith_short_12: GNHIISQPIXK7 · pith_short_16: GNHIISQPIXK7RQSC · pith_short_8: GNHIISQP

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/GNHIISQPIXK7RQSCKLBALFG57X \
  | 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: 334e844a0f45d5f8c24252c20594ddfdec51198cfe2ff3acabace22b916e190c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1906759ba00324c41638c4823bb177dc6ee4c47f8ea36390c5bd51d3a1e7c78b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-31T15:48:01Z",
    "title_canon_sha256": "abe4a0b83d09608175dbc6fdf0e9f673a3d0d63464d20342100e6ba0ae316b5c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.29555",
    "kind": "arxiv",
    "version": 1
  }
}