Pith Number

pith:T2FV5ZT5

pith:2026:T2FV5ZT5FWIHV37REKZ4PXOEDI

not attested not anchored not stored refs pending

Spectral Gap for the Binary Fixed-Margin Swap Chain

Guanyang Wang, Qian Qin, Weibo Fu

arxiv:2606.22636 v1 · 2026-06-21 · math.PR · cs.DS · math.CO · stat.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T2FV5ZT5FWIHV37REKZ4PXOEDI}

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	2026-06-23T02:13:43.697453Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e8b5ee67d2d907aeff122b3c7ddc41a219a1d80e2735e2f21a8d5adb744eb54

Aliases

arxiv: 2606.22636 · arxiv_version: 2606.22636v1 · doi: 10.48550/arxiv.2606.22636 · pith_short_12: T2FV5ZT5FWIH · pith_short_16: T2FV5ZT5FWIHV37R · pith_short_8: T2FV5ZT5

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/T2FV5ZT5FWIHV37REKZ4PXOEDI \
  | 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: 9e8b5ee67d2d907aeff122b3c7ddc41a219a1d80e2735e2f21a8d5adb744eb54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5da36210e5d4dc51e77e54420a5487ab38671c701e7c0a25720981e3412e3814",
    "cross_cats_sorted": [
      "cs.DS",
      "math.CO",
      "stat.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-21T18:46:59Z",
    "title_canon_sha256": "b7eb4d0fa023a04fec9d791e543879dd2bfd776825e3aa5e74a86c88fe954587"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.22636",
    "kind": "arxiv",
    "version": 1
  }
}