Pith Number

pith:TTK2ZQEV

pith:2018:TTK2ZQEVFNSBANSYPR3IMJP3AI

not attested not anchored not stored refs pending

Non vanishing of theta functions and sets of small multiplicative energy

Marc Munsch

arxiv:1810.05684 v1 · 2018-10-12 · 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{TTK2ZQEVFNSBANSYPR3IMJP3AI}

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	2026-05-18T00:03:27.246307Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9cd5acc0952b641036587c768625fb023b67ffb0f2c009b8175e2eac0c4a85a8

Aliases

arxiv: 1810.05684 · arxiv_version: 1810.05684v1 · doi: 10.48550/arxiv.1810.05684 · pith_short_12: TTK2ZQEVFNSB · pith_short_16: TTK2ZQEVFNSBANSY · pith_short_8: TTK2ZQEV

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/TTK2ZQEVFNSBANSYPR3IMJP3AI \
  | 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: 9cd5acc0952b641036587c768625fb023b67ffb0f2c009b8175e2eac0c4a85a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3cd9614120124a61849cd6c54ce80ef34be7a7ef0c9cada6209b84c638a04627",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-10-12T19:08:39Z",
    "title_canon_sha256": "07c4bdcd50e2a09fed4571702abc544374f99c0a6e9bbb75501fb58257fd49d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.05684",
    "kind": "arxiv",
    "version": 1
  }
}