Pith Number

pith:V5MZO4XI

pith:2017:V5MZO4XISILEMUVAUXVFTIMB6B

not attested not anchored not stored refs pending

On congruences involving product of variables from short intervals

M. Z. Garaev

arxiv:1701.07119 v1 · 2017-01-25 · 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{V5MZO4XISILEMUVAUXVFTIMB6B}

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	2026-05-18T00:52:07.451083Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af599772e892164652a0a5ea59a181f07f3c80a26ab7a3a0f0d468df9c87755a

Aliases

arxiv: 1701.07119 · arxiv_version: 1701.07119v1 · doi: 10.48550/arxiv.1701.07119 · pith_short_12: V5MZO4XISILE · pith_short_16: V5MZO4XISILEMUVA · pith_short_8: V5MZO4XI

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/V5MZO4XISILEMUVAUXVFTIMB6B \
  | 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: af599772e892164652a0a5ea59a181f07f3c80a26ab7a3a0f0d468df9c87755a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b629ec594f0f05175b09e11ddb1c78f97b542d59d19f4ac45783cd1b6475111c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-01-25T00:51:16Z",
    "title_canon_sha256": "99497402e0f020be1b82d1f858237fd8ab89c05f64e690c73cacfc9c83e91507"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.07119",
    "kind": "arxiv",
    "version": 1
  }
}