Pith Number

pith:5ELU64ZJ

pith:2007:5ELU64ZJI6GSLW4ZFKZZVGQHBJ

not attested not anchored not stored refs pending

The modular multiplication operator and the quantized bakers maps

Arul Lakshminarayan

arxiv:0707.2155 v1 · 2007-07-14 · quant-ph · nlin.CD

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5ELU64ZJI6GSLW4ZFKZZVGQHBJ}

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	2026-05-18T04:16:39.762341Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9174f7329478d25db992ab39a9a070a46bc069f4acf2bc70d93e039ad8bdb2e

Aliases

arxiv: 0707.2155 · arxiv_version: 0707.2155v1 · doi: 10.48550/arxiv.0707.2155 · pith_short_12: 5ELU64ZJI6GS · pith_short_16: 5ELU64ZJI6GSLW4Z · pith_short_8: 5ELU64ZJ

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/5ELU64ZJI6GSLW4ZFKZZVGQHBJ \
  | 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: e9174f7329478d25db992ab39a9a070a46bc069f4acf2bc70d93e039ad8bdb2e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5988b66cb530ca89a055ec8d559f5c55707e72f2b416bb4b1cc412ae479450ab",
    "cross_cats_sorted": [
      "nlin.CD"
    ],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2007-07-14T14:40:33Z",
    "title_canon_sha256": "48199199d36edae7a8777e3bc83d5a046700b2228561038f33642e8ed2145743"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0707.2155",
    "kind": "arxiv",
    "version": 1
  }
}