Pith Number

pith:STQUOIRN

pith:2009:STQUOIRN77EJG2DZVPJDMFFS23

not attested not anchored not stored refs pending

Sum-product phenomena in F_p: a brief introduction

Ben Green

arxiv:0904.2075 v1 · 2009-04-14 · math.NT · 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{STQUOIRN77EJG2DZVPJDMFFS23}

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.

Cited by

1 paper in Pith

Fourier decay of equilibrium states and the Fibonacci Hamiltonian

Receipt and verification

First computed	2026-07-04T15:41:09.592935Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

94e147222dffc8936879abd23614b2d6d962cb21b28dadfecf4fafc260c1c76b

Aliases

arxiv: 0904.2075 · arxiv_version: 0904.2075v1 · doi: 10.48550/arxiv.0904.2075 · pith_short_12: STQUOIRN77EJ · pith_short_16: STQUOIRN77EJG2DZ · pith_short_8: STQUOIRN

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/STQUOIRN77EJG2DZVPJDMFFS23 \
  | 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: 94e147222dffc8936879abd23614b2d6d962cb21b28dadfecf4fafc260c1c76b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8daa15d5b0c569f50006af2e351a4f251e5251a0f32f87d83ce62a44118f6587",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-04-14T09:19:46Z",
    "title_canon_sha256": "917dd416b84f823bc7e9214dd7b12eb0ee4c9be3c563a7249ae6fb8a8b1ff5fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.2075",
    "kind": "arxiv",
    "version": 1
  }
}