Pith Number

pith:TIULIH4H

pith:2017:TIULIH4H4HLR423WJO6QWC3LMT

not attested not anchored not stored refs pending

New results on sum-product type growth over fields

Brendan Murphy, Giorgis Petridis, Ilya D. Shkredov, Misha Rudnev, Oliver Roche-Newton

arxiv:1702.01003 v5 · 2017-02-03 · math.CO · 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{TIULIH4H4HLR423WJO6QWC3LMT}

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	2026-05-17T23:45:41.419193Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a28b41f87e1d71e6b764bbd0b0b6b64c89270dc0d38795b4ce37455433ba8b3

Aliases

arxiv: 1702.01003 · arxiv_version: 1702.01003v5 · doi: 10.48550/arxiv.1702.01003 · pith_short_12: TIULIH4H4HLR · pith_short_16: TIULIH4H4HLR423W · pith_short_8: TIULIH4H

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/TIULIH4H4HLR423WJO6QWC3LMT \
  | 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: 9a28b41f87e1d71e6b764bbd0b0b6b64c89270dc0d38795b4ce37455433ba8b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "748124266c66a4d71d212ef109b6dd68b63b0d387b4626647fb201a480b10e97",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-02-03T13:39:01Z",
    "title_canon_sha256": "7741896d2c76f31b7ea1017b53dd8fc69d8ab5f368eebaf0c944a7f837475b23"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.01003",
    "kind": "arxiv",
    "version": 5
  }
}