Pith Number

pith:DRKA3KGW

pith:2009:DRKA3KGWTF7Z5FKEXLNUTWHXSU

not attested not anchored not stored refs pending

On Modular Inverses of Cyclotomic Polynomials and the Magnitude of their Coefficients

Clement Dunand

arxiv:0907.5543 v2 · 2009-07-31 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DRKA3KGWTF7Z5FKEXLNUTWHXSU}

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	2026-05-17T23:53:19.982086Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c540da8d6997f9e9544badb49d8f795210ce5e6a78309f2b9ef73bb86954a87

Aliases

arxiv: 0907.5543 · arxiv_version: 0907.5543v2 · doi: 10.48550/arxiv.0907.5543 · pith_short_12: DRKA3KGWTF7Z · pith_short_16: DRKA3KGWTF7Z5FKE · pith_short_8: DRKA3KGW

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/DRKA3KGWTF7Z5FKEXLNUTWHXSU \
  | 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: 1c540da8d6997f9e9544badb49d8f795210ce5e6a78309f2b9ef73bb86954a87

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "316ba24d2a29bd4232f157cdd05908c1c928cdf6aff303b35af722801b4d1123",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-07-31T14:39:33Z",
    "title_canon_sha256": "a8455cb6caabbcf167c0b1896beeda4988a8bc3ebeb84fd764b8ac8114491bc2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.5543",
    "kind": "arxiv",
    "version": 2
  }
}