Pith Number

pith:W7M22UOB

pith:2020:W7M22UOBAX3YK4HYMIVAXY34VC

not attested not anchored not stored refs pending

Effective bounds on multiplicatively dependent orbits of integer polynomials modulo S-integers

Igor E. Shparlinski, Ray Li

arxiv:2001.09721 v1 · 2020-01-27 · math.NT · math.DS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W7M22UOBAX3YK4HYMIVAXY34VC}

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	2026-07-05T00:36:02.835687Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7d9ad51c105f78570f8622a0be37ca8b24f961d14dbadf69a8239c68d7fe06f

Aliases

arxiv: 2001.09721 · arxiv_version: 2001.09721v1 · doi: 10.48550/arxiv.2001.09721 · pith_short_12: W7M22UOBAX3Y · pith_short_16: W7M22UOBAX3YK4HY · pith_short_8: W7M22UOB

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/W7M22UOBAX3YK4HYMIVAXY34VC \
  | 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: b7d9ad51c105f78570f8622a0be37ca8b24f961d14dbadf69a8239c68d7fe06f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "caf7d6cc7d20fdc9dca344743b907e51d5b2d31cf6168c9b6e925e8f77c3f596",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2020-01-27T12:43:42Z",
    "title_canon_sha256": "1f55ffb1d325f04463f78953313a1a4cc3cc6fe2479408ebdce0aebd080a13d4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2001.09721",
    "kind": "arxiv",
    "version": 1
  }
}