Pith Number

pith:TH75VT3B

pith:2007:TH75VT3BEW22UHN22VW5FYJPKS

not attested not anchored not stored refs pending

Haar expectations of ratios of random characteristic polynomials

A. Huckleberry, A. Puettmann, M.R. Zirnbauer

arxiv:0709.1215 v2 · 2007-09-09 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TH75VT3BEW22UHN22VW5FYJPKS}

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	2026-05-18T01:22:54.605723Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

99ffdacf6125b5aa1dbad56dd2e12f54b5d6fb34caf23d2bc7aa1a9817d6453b

Aliases

arxiv: 0709.1215 · arxiv_version: 0709.1215v2 · doi: 10.48550/arxiv.0709.1215 · pith_short_12: TH75VT3BEW22 · pith_short_16: TH75VT3BEW22UHN2 · pith_short_8: TH75VT3B

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/TH75VT3BEW22UHN22VW5FYJPKS \
  | 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: 99ffdacf6125b5aa1dbad56dd2e12f54b5d6fb34caf23d2bc7aa1a9817d6453b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b785250655d5cc62fa05ddd1a27ad91537815ac5c36accc27a328834cd3bbf6",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2007-09-09T14:02:25Z",
    "title_canon_sha256": "1868ac14e1a2e6661545e20ded33f59a0565f7ea2ff78effdf6bf33cec7f8054"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.1215",
    "kind": "arxiv",
    "version": 2
  }
}