Pith Number

pith:VE2E2HOX

pith:2012:VE2E2HOXSNQAKN25NNWL2MKLZF

not attested not anchored not stored refs pending

An inverse theorem for Gowers norms of trace functions over prime fields

Emmanuel Kowalski, \'Etienne Fouvry, Philippe Michel

arxiv:1211.3282 v3 · 2012-11-14 · 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{VE2E2HOXSNQAKN25NNWL2MKLZF}

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	2026-05-18T03:34:02.705553Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9344d1dd7936005375d6b6cbd314bc96e3faf50b14d0b65cc37636d63ad28b6

Aliases

arxiv: 1211.3282 · arxiv_version: 1211.3282v3 · doi: 10.48550/arxiv.1211.3282 · pith_short_12: VE2E2HOXSNQA · pith_short_16: VE2E2HOXSNQAKN25 · pith_short_8: VE2E2HOX

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/VE2E2HOXSNQAKN25NNWL2MKLZF \
  | 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: a9344d1dd7936005375d6b6cbd314bc96e3faf50b14d0b65cc37636d63ad28b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6ad54d085679040e57edd5c5cb16271ec24f636c9b018a728c7d486e3f65be70",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-11-14T12:04:58Z",
    "title_canon_sha256": "2b3e208e5ebce5b20f1bc3e67b734ca4127c13b01709d275f388990e43aea82f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.3282",
    "kind": "arxiv",
    "version": 3
  }
}