Pith Number

pith:TRKUCDVA

pith:2026:TRKUCDVAF6UP252VF2NOIHNVYO

not attested not anchored not stored refs pending

Banach-valued graph limits: Graphon representability and Banach-space structure

Motoki Otsuka

arxiv:2607.26687 v1 · 2026-07-29 · math.FA · 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{TRKUCDVAF6UP252VF2NOIHNVYO}

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	2026-07-30T01:21:56.240778Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

9c55410ea02fa8fd77552e9ae41db5c397d546395e4b3cb1b3390fb68f9e4ccc

Aliases

arxiv: 2607.26687 · arxiv_version: 2607.26687v1 · doi: 10.48550/arxiv.2607.26687 · pith_short_12: TRKUCDVAF6UP · pith_short_16: TRKUCDVAF6UP252V · pith_short_8: TRKUCDVA

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/TRKUCDVAF6UP252VF2NOIHNVYO \
  | 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: 9c55410ea02fa8fd77552e9ae41db5c397d546395e4b3cb1b3390fb68f9e4ccc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "98232dad5ef09a02f0f5ff6fd5edbb6cf07e7a71b93a69e6e1ce6c5558559230",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-07-29T09:34:49Z",
    "title_canon_sha256": "384ade7c36b921dc3c561c8303f4b0268529ff5d6c08dae812cec9daeb565674"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.26687",
    "kind": "arxiv",
    "version": 1
  }
}