Pith Number

pith:CYPUYFRF

pith:2026:CYPUYFRF2LJWFZND5RWSEGOSER

not attested not anchored not stored refs pending

Do Hopfield Networks Dream of Stored Patterns? A Statistical-Mechanical Theory of Dreaming in Multidirectional Associative Memories

Adriano Barra, Andrea Ladiana, Fabrizio Durante, Michela Marra Solazzo

arxiv:2605.13721 v1 · 2026-05-13 · cond-mat.dis-nn

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CYPUYFRF2LJWFZND5RWSEGOSER}

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	2026-05-18T02:44:16.653428Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

161f4c1625d2d362e5a3ec6d2219d22464d62722c1b4ae6aceea40bc3fa061ef

Aliases

arxiv: 2605.13721 · arxiv_version: 2605.13721v1 · doi: 10.48550/arxiv.2605.13721 · pith_short_12: CYPUYFRF2LJW · pith_short_16: CYPUYFRF2LJWFZND · pith_short_8: CYPUYFRF

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/CYPUYFRF2LJWFZND5RWSEGOSER \
  | 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: 161f4c1625d2d362e5a3ec6d2219d22464d62722c1b4ae6aceea40bc3fa061ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ccc744c40031f7f5e873ab5ba86b9a7bcf17a432fa216d6e2f65b412f7d9ea22",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.dis-nn",
    "submitted_at": "2026-05-13T16:05:36Z",
    "title_canon_sha256": "d86da0590bec05b4b8a77ce0dc69adbf18c8986dc42141478f839a246f104995"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13721",
    "kind": "arxiv",
    "version": 1
  }
}