Pith Number

pith:QC6KOSOK

pith:2025:QC6KOSOKGVYP26643RRMHACFQS

not attested not anchored not stored refs pending

Stark-Coleman Invariants and Quantum Lower Bounds: An Integrated Framework for Real Quadratic Fields

Chenglian Liu, Ruopengyu Xu

arxiv:2506.07640 v1 · 2025-06-09 · math.NT · cs.CR · math.GR · 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{QC6KOSOKGVYP26643RRMHACFQS}

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	2026-07-05T11:27:30.673916Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80bca749ca3570fd7bdcdc62c3804584987262dfd260849742a0b720de042b4e

Aliases

arxiv: 2506.07640 · arxiv_version: 2506.07640v1 · doi: 10.48550/arxiv.2506.07640 · pith_short_12: QC6KOSOKGVYP · pith_short_16: QC6KOSOKGVYP2664 · pith_short_8: QC6KOSOK

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/QC6KOSOKGVYP26643RRMHACFQS \
  | 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: 80bca749ca3570fd7bdcdc62c3804584987262dfd260849742a0b720de042b4e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33d21e132f880d6ce62a3e53c2b6d3d510cb06ed68dd68a5d59c0f3fe1bcf8c2",
    "cross_cats_sorted": [
      "cs.CR",
      "math.GR",
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-06-09T11:06:17Z",
    "title_canon_sha256": "b8a293f4dcd52e5bc80622fae5c35476c948466512f85bc65e8ff761af677957"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.07640",
    "kind": "arxiv",
    "version": 1
  }
}