Pith Number

pith:MRXEZN6X

pith:2024:MRXEZN6X3NUKMNHFSAQ332Z3DN

not attested not anchored not stored refs pending

On the singularity probability of random circulant Bernoulli matrices

Niklas Miller

arxiv:2411.17577 v1 · 2024-11-26 · math.CO · 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{MRXEZN6X3NUKMNHFSAQ332Z3DN}

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	2026-07-05T09:40:49.183248Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

646e4cb7d7db68a634e59021bdeb3b1b6f893fc8c2eaba86947a61fe5b9625ba

Aliases

arxiv: 2411.17577 · arxiv_version: 2411.17577v1 · doi: 10.48550/arxiv.2411.17577 · pith_short_12: MRXEZN6X3NUK · pith_short_16: MRXEZN6X3NUKMNHF · pith_short_8: MRXEZN6X

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/MRXEZN6X3NUKMNHFSAQ332Z3DN \
  | 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: 646e4cb7d7db68a634e59021bdeb3b1b6f893fc8c2eaba86947a61fe5b9625ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c3d2aea0967d3d7beaaf3323f61bbbd459e16e1740a851a2c4c3d899e212232",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-11-26T16:41:59Z",
    "title_canon_sha256": "9f55cb369ba767e54197ce167a0d54ceaa5d362827df685661d2f3ba68edff08"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.17577",
    "kind": "arxiv",
    "version": 1
  }
}