Pith Number

pith:TTUBJYFX

pith:2026:TTUBJYFXCYRETLQCGCFD4GPVXY

not attested not anchored not stored refs pending

Using Tanner Spectral Reduction to Improve Multi-Layer Optical Lattice Routing for Hypergraph-Product and Bivariate Bicycle qLDPC Codes

Joshua M. Courtney

arxiv:2607.06177 v1 · 2026-07-07 · quant-ph · cs.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TTUBJYFXCYRETLQCGCFD4GPVXY}

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	2026-07-08T01:19:16.659700Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ce814e0b7162249ae02308a3e19f5be326d0c4183507af440e72167e3d6c147

Aliases

arxiv: 2607.06177 · arxiv_version: 2607.06177v1 · doi: 10.48550/arxiv.2607.06177 · pith_short_12: TTUBJYFXCYRE · pith_short_16: TTUBJYFXCYRETLQC · pith_short_8: TTUBJYFX

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/TTUBJYFXCYRETLQCGCFD4GPVXY \
  | 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: 9ce814e0b7162249ae02308a3e19f5be326d0c4183507af440e72167e3d6c147

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "946d264b045b5333a90ae62eb55cce92b97a93c5f968c130c8e111b7fbe85e08",
    "cross_cats_sorted": [
      "cs.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-07-07T11:54:26Z",
    "title_canon_sha256": "4010d91c662534201a507d2d97e4fce05198df074a3ebcda9474761b34246658"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.06177",
    "kind": "arxiv",
    "version": 1
  }
}