Pith Number

pith:I3VBZ3NE

pith:2016:I3VBZ3NEOK7RTTDEUXEBM2D6N7

not attested not anchored not stored refs pending

An application of the sum-product phenomenon to sets having no solutions of several linear equations

Ilya D. Shkredov

arxiv:1609.06489 v2 · 2016-09-21 · 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{I3VBZ3NEOK7RTTDEUXEBM2D6N7}

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	2026-05-18T01:01:35.706871Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46ea1ceda472bf19cc64a5c816687e6fe3c02f5a0f91e52de23a38b002eda699

Aliases

arxiv: 1609.06489 · arxiv_version: 1609.06489v2 · doi: 10.48550/arxiv.1609.06489 · pith_short_12: I3VBZ3NEOK7R · pith_short_16: I3VBZ3NEOK7RTTDE · pith_short_8: I3VBZ3NE

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/I3VBZ3NEOK7RTTDEUXEBM2D6N7 \
  | 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: 46ea1ceda472bf19cc64a5c816687e6fe3c02f5a0f91e52de23a38b002eda699

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1aa16d45a557461d0fb57148dd17d436244e7e79f20ac5bdb79d9db55e2bcf9e",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-09-21T10:25:45Z",
    "title_canon_sha256": "8c986dd092f00bee41206865303c8f9f196d134e8f086485a56f828ec9845037"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.06489",
    "kind": "arxiv",
    "version": 2
  }
}