Pith Number

pith:ZSJKSI5D

pith:2017:ZSJKSI5D5T6Z4YVIFNQRAMKXIT

not attested not anchored not stored refs pending

Certifying numerical estimates of spectral gaps

Marek Kaluba, Piotr Nowak

arxiv:1703.09680 v3 · 2017-03-28 · math.GR · 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{ZSJKSI5D5T6Z4YVIFNQRAMKXIT}

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	2026-05-18T00:33:20.941234Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc92a923a3ecfd9e62a82b6110315744f2692784ecb557cc1b65b4fac59f2a8a

Aliases

arxiv: 1703.09680 · arxiv_version: 1703.09680v3 · doi: 10.48550/arxiv.1703.09680 · pith_short_12: ZSJKSI5D5T6Z · pith_short_16: ZSJKSI5D5T6Z4YVI · pith_short_8: ZSJKSI5D

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/ZSJKSI5D5T6Z4YVIFNQRAMKXIT \
  | 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: cc92a923a3ecfd9e62a82b6110315744f2692784ecb557cc1b65b4fac59f2a8a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f06d4878154443ae4d837e2da9a7a238595d2c562daa7bc1f95f6ea0cc8fe05",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-03-28T17:28:50Z",
    "title_canon_sha256": "ab5e25948ccd8ff45005bb2d0400f47077e5f38757daa1085b7bbba296ab404a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1703.09680",
    "kind": "arxiv",
    "version": 3
  }
}