Pith Number

pith:OVDK24BP

pith:2018:OVDK24BPQLKWBMUYBIIU5ZNZ3Y

not attested not anchored not stored refs pending

Double exponential sums and congruences with intervals and exponential functions modulo a prime

M. Z. Garaev

arxiv:1810.06341 v1 · 2018-10-15 · 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{OVDK24BPQLKWBMUYBIIU5ZNZ3Y}

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	2026-05-18T00:03:20.768630Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7546ad702f82d560b2980a114ee5b9de30496e981cb4f44c603afe85c14605ae

Aliases

arxiv: 1810.06341 · arxiv_version: 1810.06341v1 · doi: 10.48550/arxiv.1810.06341 · pith_short_12: OVDK24BPQLKW · pith_short_16: OVDK24BPQLKWBMUY · pith_short_8: OVDK24BP

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/OVDK24BPQLKWBMUYBIIU5ZNZ3Y \
  | 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: 7546ad702f82d560b2980a114ee5b9de30496e981cb4f44c603afe85c14605ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7701f5e2ea3e61c1368c4d1722626c155d4dff569a86581af9d7935bf5332af7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-10-15T13:23:40Z",
    "title_canon_sha256": "158a3d0c6c8357902bd82d980460fe25f8ee6ab6830fada44727acb80472606e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.06341",
    "kind": "arxiv",
    "version": 1
  }
}