Pith Number

pith:CAXNDWIU

pith:2026:CAXNDWIUVGOFD2ASMEYUEWEJHO

not attested not anchored not stored refs pending

Random unitary circuits with constant spectral gap

Jeongwan Haah, Tim Baer

arxiv:2607.20919 v1 · 2026-07-23 · quant-ph · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CAXNDWIUVGOFD2ASMEYUEWEJHO}

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	2026-07-24T01:23:40.726718Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

102ed1d914a99c51e81261314258893b9a6f3418ff49e3496dd6551846999c18

Aliases

arxiv: 2607.20919 · arxiv_version: 2607.20919v1 · doi: 10.48550/arxiv.2607.20919 · pith_short_12: CAXNDWIUVGOF · pith_short_16: CAXNDWIUVGOFD2AS · pith_short_8: CAXNDWIU

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/CAXNDWIUVGOFD2ASMEYUEWEJHO \
  | 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: 102ed1d914a99c51e81261314258893b9a6f3418ff49e3496dd6551846999c18

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "145493aea1736a927f10ec3291b51636e63d740ae718c30c30008e0a71721f4f",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-07-23T04:56:09Z",
    "title_canon_sha256": "14b7979a49836210b89648ae9a124c42d1b91332de43aff300bb02c8ee4913ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.20919",
    "kind": "arxiv",
    "version": 1
  }
}