Pith Number

pith:TBWQCI2Z

pith:2012:TBWQCI2Z55WQI4KGIZBXDPF4VD

not attested not anchored not stored refs pending

Multiplicative Congruences with Variables from Short Intervals

Igor E. Shparlinski, Jean Bourgain, Moubariz Z. Garaev, Sergei V.Konyagin

arxiv:1210.6429 v1 · 2012-10-24 · 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{TBWQCI2Z55WQI4KGIZBXDPF4VD}

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	2026-05-18T03:42:24.867434Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

986d012359ef6d047146464371bcbca8d4e42bd6631756f63857095646555916

Aliases

arxiv: 1210.6429 · arxiv_version: 1210.6429v1 · doi: 10.48550/arxiv.1210.6429 · pith_short_12: TBWQCI2Z55WQ · pith_short_16: TBWQCI2Z55WQI4KG · pith_short_8: TBWQCI2Z

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/TBWQCI2Z55WQI4KGIZBXDPF4VD \
  | 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: 986d012359ef6d047146464371bcbca8d4e42bd6631756f63857095646555916

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "62706d2621495c44186555d0b8a6529291f2670326f80589bb5f85e26fea1901",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-10-24T03:35:38Z",
    "title_canon_sha256": "4b0374a200f93390fab71e31a07643e592725450e2559f6a45272dfd09a971a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.6429",
    "kind": "arxiv",
    "version": 1
  }
}