Pith Number

pith:5BJDO2NY

pith:2012:5BJDO2NYI72TUXFG4554CTJL3M

not attested not anchored not stored refs pending

Complete positivity of the map from a basis to its dual basis

Fred Shultz, Vern I. Paulsen

arxiv:1212.4787 v1 · 2012-12-19 · quant-ph · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5BJDO2NYI72TUXFG4554CTJL3M}

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	2026-05-18T01:52:30.319431Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e8523769b847f53a5ca6e77bc14d2bdb16a655dfdf171553269157d29ab0a465

Aliases

arxiv: 1212.4787 · arxiv_version: 1212.4787v1 · doi: 10.48550/arxiv.1212.4787 · pith_short_12: 5BJDO2NYI72T · pith_short_16: 5BJDO2NYI72TUXFG · pith_short_8: 5BJDO2NY

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/5BJDO2NYI72TUXFG4554CTJL3M \
  | 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: e8523769b847f53a5ca6e77bc14d2bdb16a655dfdf171553269157d29ab0a465

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4099138d91849171f72862d2e3c66e09c1da8997828ee8453cedfbcef419f502",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2012-12-19T18:35:45Z",
    "title_canon_sha256": "af9655ded6a6d4d774b5d01e121ef2792b3d27cc527c7836264a0c741b4eb2a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.4787",
    "kind": "arxiv",
    "version": 1
  }
}