Pith Number

pith:CUTWRKDP

pith:2012:CUTWRKDPCBY5AYQ6ANEEUHHHDJ

not attested not anchored not stored refs pending

Linear Dependencies in Weyl-Heisenberg Orbits

D. M. Appleby, Hoan Bui Dang, Ingemar Bengtsson, Kate Blanchfield

arxiv:1211.0215 v2 · 2012-11-01 · math-ph · math.MP · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CUTWRKDPCBY5AYQ6ANEEUHHHDJ}

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	2026-05-18T03:05:44.666972Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

152768a86f1071d0621e03484a1ce71a687ca89c8c245126b5eb17a9eafbd2e1

Aliases

arxiv: 1211.0215 · arxiv_version: 1211.0215v2 · doi: 10.48550/arxiv.1211.0215 · pith_short_12: CUTWRKDPCBY5 · pith_short_16: CUTWRKDPCBY5AYQ6 · pith_short_8: CUTWRKDP

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/CUTWRKDPCBY5AYQ6ANEEUHHHDJ \
  | 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: 152768a86f1071d0621e03484a1ce71a687ca89c8c245126b5eb17a9eafbd2e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00e4fce8eb9ad6cf0dbaf8aeabefd6f7ee51869f2dd517b8e39a3e6b862763cc",
    "cross_cats_sorted": [
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-11-01T16:17:08Z",
    "title_canon_sha256": "88f92385e85450463325c80fafe87b02b60965ce4604eb4d7f4ef6d546c47594"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.0215",
    "kind": "arxiv",
    "version": 2
  }
}