Pith Number

pith:ZBJK3CD3

pith:2009:ZBJK3CD3BLWQDPG4K4I2E6CVY5

not attested not anchored not stored refs pending

A gradient system on the quantum information space realizing the averaged learning equation of Hebb type

Hiromi Yuya, Yoshio Uwano

arxiv:0912.3328 v1 · 2009-12-17 · math.DS · math-ph · 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{ZBJK3CD3BLWQDPG4K4I2E6CVY5}

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	2026-05-18T02:55:48.811124Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c852ad887b0aed01bcdc5711a27855c76b89f9f4730581603d4eadc801aa7932

Aliases

arxiv: 0912.3328 · arxiv_version: 0912.3328v1 · doi: 10.48550/arxiv.0912.3328 · pith_short_12: ZBJK3CD3BLWQ · pith_short_16: ZBJK3CD3BLWQDPG4 · pith_short_8: ZBJK3CD3

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/ZBJK3CD3BLWQDPG4K4I2E6CVY5 \
  | 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: c852ad887b0aed01bcdc5711a27855c76b89f9f4730581603d4eadc801aa7932

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e5a987221d2967ca608421d5982f285c75bd33eb489fb5bd1b92f91fc879397",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2009-12-17T07:31:36Z",
    "title_canon_sha256": "5047c0e98ade02fb4905dd0b4d61104579be68891b28d56717844a97880cefcd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.3328",
    "kind": "arxiv",
    "version": 1
  }
}