Pith. sign in
Pith Number

pith:WGTP4W7H

pith:2026:WGTP4W7H4EE2XNYBMJRAXSI2DU
not attested not anchored not stored refs pending

Selfless C*-correspondences, operator valued C*-probability spaces and completely positive maps

David Gao, Gregory Patchell, Leonel Robert, Marius Junge, Srivatsav Kunnawalkam Elayavalli

arxiv:2607.20361 v1 · 2026-07-22 · 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{WGTP4W7H4EE2XNYBMJRAXSI2DU}

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 2026-07-23T01:25:16.639059Z
Builder pith-number-builder-2026-05-17-v1
Signature Pith Ed25519 (pith-v1-2026-05) · public key
Schema pith-number/v1.0

Canonical hash

b1a6fe5be7e109abb70162620bc91a1d3ba923442e0c35debf4449941339c02c

Aliases

arxiv: 2607.20361 · arxiv_version: 2607.20361v1 · doi: 10.48550/arxiv.2607.20361 · pith_short_12: WGTP4W7H4EE2 · pith_short_16: WGTP4W7H4EE2XNYB · pith_short_8: WGTP4W7H
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/WGTP4W7H4EE2XNYBMJRAXSI2DU \
  | 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: b1a6fe5be7e109abb70162620bc91a1d3ba923442e0c35debf4449941339c02c
Canonical record JSON 
{
  "metadata": {
    "abstract_canon_sha256": "ce984f1d8983858202430104e3aae6532929dd71fb6aa4c3ae787b4f803947af",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-07-22T16:51:01Z",
    "title_canon_sha256": "8ad8134f125106e8712f195c4ba1c27cd8c4fe88978c9a8dd0e6f73b8ad99e11"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.20361",
    "kind": "arxiv",
    "version": 1
  }
}