Pith Number

pith:J3R3MQ5M

pith:2026:J3R3MQ5MST3G47M4V3KFQNFUN7

not attested not anchored not stored refs pending

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces

George Em Karniadakis, Khemraj Shukla

arxiv:2608.06428 v1 · 2026-08-05 · cs.LG · math-ph · math.GN · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J3R3MQ5MST3G47M4V3KFQNFUN7}

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	2026-08-10T01:10:38.686828Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ee3b643ac94f66e7d9caed45834b46ff9c8a40237fa3e4aed31b91031e29442

Aliases

arxiv: 2608.06428 · arxiv_version: 2608.06428v1 · doi: 10.48550/arxiv.2608.06428 · pith_short_12: J3R3MQ5MST3G · pith_short_16: J3R3MQ5MST3G47M4 · pith_short_8: J3R3MQ5M

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/J3R3MQ5MST3G47M4V3KFQNFUN7 \
  | 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: 4ee3b643ac94f66e7d9caed45834b46ff9c8a40237fa3e4aed31b91031e29442

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fcae6b224e8b5bb6489dd9737359f1c1d23f3e452c160d8a92909acd55ef5a0b",
    "cross_cats_sorted": [
      "math-ph",
      "math.GN",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-08-05T20:23:32Z",
    "title_canon_sha256": "30ccceb8c72efb26ba75bc17e016263544b6a6265a9d55f264930806696dec12"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.06428",
    "kind": "arxiv",
    "version": 1
  }
}