Pith Number

pith:NGKDVUMJ

pith:2026:NGKDVUMJWF6DHSS5ZKWOXNMIPI

not attested not anchored not stored refs pending

Sparse positive maps on qutrits with exact nondecomposability thresholds and PPT-entanglement transitions

Angela Rosy Morgillo, Chiara Macchiavello, Davide Poderini, Fabio Anselmi, Fabio Benatti, Massimiliano F. Sacchi

arxiv:2606.19765 v1 · 2026-06-18 · 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{NGKDVUMJWF6DHSS5ZKWOXNMIPI}

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	2026-06-19T16:12:34.538341Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69943ad189b17c33ca5dcaacebb5887a2ef2817786d05ff981c4a047e748aa8b

Aliases

arxiv: 2606.19765 · arxiv_version: 2606.19765v1 · doi: 10.48550/arxiv.2606.19765 · pith_short_12: NGKDVUMJWF6D · pith_short_16: NGKDVUMJWF6DHSS5 · pith_short_8: NGKDVUMJ

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/NGKDVUMJWF6DHSS5ZKWOXNMIPI \
  | 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: 69943ad189b17c33ca5dcaacebb5887a2ef2817786d05ff981c4a047e748aa8b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4667057322d35191bda5d88596e868bf841ecd2d89ebcb3bae843d9ad87586a5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-06-18T03:56:21Z",
    "title_canon_sha256": "59bc64b21b6c91af06ac7ec4d8fc0492e523d133cc4cbb75f358210732bc8c57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.19765",
    "kind": "arxiv",
    "version": 1
  }
}