Pith Number

pith:3OC5LOXA

pith:2025:3OC5LOXADVRIA7OKIZVJC3JGAO

not attested not anchored not stored refs pending

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits

Christopher J. Hillar, Kedar Karhadker, Michael Murray, Tenzin Chan

arxiv:2512.14338 v3 · 2025-12-16 · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3OC5LOXADVRIA7OKIZVJC3JGAO}

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	2026-06-05T01:15:18.449025Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db85d5bae01d62807dca466a916d2603b38d5f21fb896daf8b02a8d46b4999de

Aliases

arxiv: 2512.14338 · arxiv_version: 2512.14338v3 · doi: 10.48550/arxiv.2512.14338 · pith_short_12: 3OC5LOXADVRI · pith_short_16: 3OC5LOXADVRIA7OK · pith_short_8: 3OC5LOXA

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/3OC5LOXADVRIA7OKIZVJC3JGAO \
  | 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: db85d5bae01d62807dca466a916d2603b38d5f21fb896daf8b02a8d46b4999de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8fa9279ae4e4699089bb718109959ba5b2a5a52ce8364846434dbf560febcb40",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-12-16T12:06:58Z",
    "title_canon_sha256": "ad26ef52b67750c7a79ee8bf504574c8b94c929477c70ff9aa2cfb8ff9b4fe1c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.14338",
    "kind": "arxiv",
    "version": 3
  }
}