Pith Number

pith:VDSW5FV4

pith:2014:VDSW5FV4IN72ZC64NM6HULFPXN

not attested not anchored not stored refs pending

New sum-product estimates for real and complex numbers

Antal Balog, Oliver Roche-Newton

arxiv:1402.5775 v1 · 2014-02-24 · 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{VDSW5FV4IN72ZC64NM6HULFPXN}

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	2026-05-18T02:58:13.686880Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8e56e96bc437fac8bdc6b3c7a2cafbb7126c39481d98f9e17deeda57e0b37a0

Aliases

arxiv: 1402.5775 · arxiv_version: 1402.5775v1 · doi: 10.48550/arxiv.1402.5775 · pith_short_12: VDSW5FV4IN72 · pith_short_16: VDSW5FV4IN72ZC64 · pith_short_8: VDSW5FV4

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/VDSW5FV4IN72ZC64NM6HULFPXN \
  | 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: a8e56e96bc437fac8bdc6b3c7a2cafbb7126c39481d98f9e17deeda57e0b37a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0a0d6500bf59a310006b9680889a8eaee952c3139e4767633731db86214ea3e",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-02-24T10:26:51Z",
    "title_canon_sha256": "3d8dc20d6b1f97b982fccedf2bd1f5ad214d2cba70916c02d85e93c8954e5fbb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1402.5775",
    "kind": "arxiv",
    "version": 1
  }
}