Pith Number

pith:QCDU63LD

pith:2025:QCDU63LDMIAOSXPT3UV4SHAXFL

not attested not anchored not stored refs pending

Explicit Construction of Approximate Kolmogorov Superpositions with C2 Smoothness

Juan Diego Toscano, Li-Lian Wang, Lunji Song, Zilan Cheng

arxiv:2508.04392 v2 · 2025-08-06 · math.NA · cs.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QCDU63LDMIAOSXPT3UV4SHAXFL}

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.

Cited by

2 papers in Pith

ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms

GRAFT-ATHENA: Self-Improving Agentic Teams for Autonomous Discovery and Evolutionary Numerical Algorithms

Receipt and verification

First computed	2026-05-20T00:02:05.809569Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80874f6d636200e95df3dd2bc91c172ac83f12a39b8ff5c8527e55468e054046

Aliases

arxiv: 2508.04392 · arxiv_version: 2508.04392v2 · doi: 10.48550/arxiv.2508.04392 · pith_short_12: QCDU63LDMIAO · pith_short_16: QCDU63LDMIAOSXPT · pith_short_8: QCDU63LD

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/QCDU63LDMIAOSXPT3UV4SHAXFL \
  | 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: 80874f6d636200e95df3dd2bc91c172ac83f12a39b8ff5c8527e55468e054046

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a931a7a732f840cd9092bd059201b17022dbc95f65d9821ce4b373b8275e8206",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2025-08-06T12:37:37Z",
    "title_canon_sha256": "8dcca7944a30c431882f16926172d568b67a16d8b564a75bce75e96dbafed6c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.04392",
    "kind": "arxiv",
    "version": 2
  }
}