Pith Number

pith:D5BNYV46

pith:2019:D5BNYV46YN5MB6PLB56E567Y6Q

not attested not anchored not stored refs pending

Some remarks on products of sets in the Heisenberg group and in the affine group

Ilya D. Shkredov

arxiv:1907.03357 v1 · 2019-07-07 · 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{D5BNYV46YN5MB6PLB56E567Y6Q}

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	2026-05-17T23:41:16.452214Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f42dc579ec37ac0f9eb0f7c4efbf8f41688389bb5aebcb8d37ba2ef685945c7

Aliases

arxiv: 1907.03357 · arxiv_version: 1907.03357v1 · doi: 10.48550/arxiv.1907.03357 · pith_short_12: D5BNYV46YN5M · pith_short_16: D5BNYV46YN5MB6PL · pith_short_8: D5BNYV46

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/D5BNYV46YN5MB6PLB56E567Y6Q \
  | 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: 1f42dc579ec37ac0f9eb0f7c4efbf8f41688389bb5aebcb8d37ba2ef685945c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7a5b86363e2c4506753e832a949e0c2c2e2d070e6ea1b5aae439a7759c3ef24",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-07-07T22:30:37Z",
    "title_canon_sha256": "ba9cb386e30ba291053ebc5cebf3edb5ed8bf8ff0c9f001a281e0b9f7bb9b66f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.03357",
    "kind": "arxiv",
    "version": 1
  }
}