Pith Number

pith:TYWA6QBD

pith:2026:TYWA6QBDPFVTJPU7QLHMNCNJYJ

not attested not anchored not stored refs pending

An upper bound for the purity of absolutely positive partial transpose states

Anh T. Tran

arxiv:2608.09832 v1 · 2026-08-10 · quant-ph · 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{TYWA6QBDPFVTJPU7QLHMNCNJYJ}

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	2026-08-11T02:25:12.580557Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e2c0f4023796b34be9f82cec689a9c267cd96cbd7a6b40433e00868a680ec3f

Aliases

arxiv: 2608.09832 · arxiv_version: 2608.09832v1 · doi: 10.48550/arxiv.2608.09832 · pith_short_12: TYWA6QBDPFVT · pith_short_16: TYWA6QBDPFVTJPU7 · pith_short_8: TYWA6QBD

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/TYWA6QBDPFVTJPU7QLHMNCNJYJ \
  | 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: 9e2c0f4023796b34be9f82cec689a9c267cd96cbd7a6b40433e00868a680ec3f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c588f361e0ce0573a6bc399affaf6ba4bec0fe6c8e869cf7c5deacc77d59e6c4",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-08-10T16:50:15Z",
    "title_canon_sha256": "0d4e869c0fe375a916f20b9cd639e4957a2a7ef6b51f5f73586abad00c1e8787"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.09832",
    "kind": "arxiv",
    "version": 1
  }
}