Pith Number

pith:MKPVTPKD

pith:2012:MKPVTPKDH3R7ZXQ3CM6SJLOZRS

not attested not anchored not stored refs pending

The number of harmonic frames of prime order

Matthew J. Hirn

arxiv:1209.0153 v1 · 2012-09-02 · math.RA · math.CA · math.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{MKPVTPKDH3R7ZXQ3CM6SJLOZRS}

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	2026-05-18T03:46:29.774831Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

629f59bd433ee3fcde1b133d24add98cbc53260689e391294dcb6ebd6fd94303

Aliases

arxiv: 1209.0153 · arxiv_version: 1209.0153v1 · doi: 10.48550/arxiv.1209.0153 · pith_short_12: MKPVTPKDH3R7 · pith_short_16: MKPVTPKDH3R7ZXQ3 · pith_short_8: MKPVTPKD

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/MKPVTPKDH3R7ZXQ3CM6SJLOZRS \
  | 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: 629f59bd433ee3fcde1b133d24add98cbc53260689e391294dcb6ebd6fd94303

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f608a469679f48256104f35f0c1b78b3cc4ef96194e645e5053a2588e3c4552",
    "cross_cats_sorted": [
      "math.CA",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2012-09-02T07:33:51Z",
    "title_canon_sha256": "e4646857946dd8a42f9fe6c8afb39cb53df6ea11f776f945f760711844a0e0d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0153",
    "kind": "arxiv",
    "version": 1
  }
}