Pith Number

pith:QMMPAQ5G

pith:2026:QMMPAQ5GVW3DNEOSZZ4QNPGJDX

not attested not anchored not stored refs pending

The reduced Hao-Ng isomorphism problem for non-degenerate product systems

Ioannis Apollon Paraskevas

arxiv:2607.17824 v1 · 2026-07-20 · math.OA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QMMPAQ5GVW3DNEOSZZ4QNPGJDX}

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	2026-07-21T02:22:02.122625Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8318f043a6adb63691d2ce7906bcc91dd969fe95268684a521176851480324f7

Aliases

arxiv: 2607.17824 · arxiv_version: 2607.17824v1 · doi: 10.48550/arxiv.2607.17824 · pith_short_12: QMMPAQ5GVW3D · pith_short_16: QMMPAQ5GVW3DNEOS · pith_short_8: QMMPAQ5G

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/QMMPAQ5GVW3DNEOSZZ4QNPGJDX \
  | 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: 8318f043a6adb63691d2ce7906bcc91dd969fe95268684a521176851480324f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dab841057fa303e3d435585af42561df0011ce2fd94b0eb0abc300482c58bb84",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-07-20T11:12:08Z",
    "title_canon_sha256": "9d3f5bc3eaf4b4c200ba1f91e87846f9e3493c63c5a38c7452fffe6163453dc0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.17824",
    "kind": "arxiv",
    "version": 1
  }
}