Pith Number

pith:DL2O75ZZ

pith:2026:DL2O75ZZ7YG3A4C6OQSVAIJWVE

not attested not anchored not stored refs pending

Structural Preservation and the Logical Expressiveness of Graph Neural Networks

Bernardo Cuenca Grau, Przemys{\l}aw Andrzej Wa{\l}\k{e}ga

arxiv:2606.17882 v1 · 2026-06-16 · cs.AI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DL2O75ZZ7YG3A4C6OQSVAIJWVE}

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	2026-06-19T16:10:42.596204Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1af4eff739fe0db0705e7425502136a9149a4da74ff93e64c5ff5ed8e0c51a44

Aliases

arxiv: 2606.17882 · arxiv_version: 2606.17882v1 · doi: 10.48550/arxiv.2606.17882 · pith_short_12: DL2O75ZZ7YG3 · pith_short_16: DL2O75ZZ7YG3A4C6 · pith_short_8: DL2O75ZZ

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/DL2O75ZZ7YG3A4C6OQSVAIJWVE \
  | 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: 1af4eff739fe0db0705e7425502136a9149a4da74ff93e64c5ff5ed8e0c51a44

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4e46cc2859a62dc06d47a0983adbe0f8abb97271b6b7b695265e9cf68a7481f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.AI",
    "submitted_at": "2026-06-16T12:57:50Z",
    "title_canon_sha256": "a55844b88b74fd98da76c280d99bf2c940e3af66d9224f82ba63a3824debb04b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.17882",
    "kind": "arxiv",
    "version": 1
  }
}