Pith Number

pith:UMMYCHMY

pith:2011:UMMYCHMYOFG5FMJDH42KECZ4RO

not attested not anchored not stored refs pending

An improved sum-product estimate over finite fields

Liangpan Li, Oliver Roche-Newton

arxiv:1106.1148 v1 · 2011-05-31 · 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{UMMYCHMYOFG5FMJDH42KECZ4RO}

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	2026-05-18T04:20:36.317310Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a319811d98714dd2b1233f34a20b3c8b85842e5dac98a6aa005180b0f0751ada

Aliases

arxiv: 1106.1148 · arxiv_version: 1106.1148v1 · doi: 10.48550/arxiv.1106.1148 · pith_short_12: UMMYCHMYOFG5 · pith_short_16: UMMYCHMYOFG5FMJD · pith_short_8: UMMYCHMY

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/UMMYCHMYOFG5FMJDH42KECZ4RO \
  | 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: a319811d98714dd2b1233f34a20b3c8b85842e5dac98a6aa005180b0f0751ada

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "515a4e2a3d0c393791ddc08cc5f76288d1cd265039a9ce673d14a878591127fa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-05-31T10:04:52Z",
    "title_canon_sha256": "6e4fe3eb3bfe4f0544830c062a613c822f41e53d2098b4f73b5cf7f06de01659"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.1148",
    "kind": "arxiv",
    "version": 1
  }
}