Pith Number

pith:VLB3TTJH

pith:2016:VLB3TTJHYCLJSWSSGUWQ4KERRQ

not attested not anchored not stored refs pending

On multiplicatively dependent vectors of algebraic numbers

Cameron L. Stewart, Francesco Pappalardi, Igor E. Shparlinski, Min Sha

arxiv:1606.02874 v1 · 2016-06-09 · 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{VLB3TTJHYCLJSWSSGUWQ4KERRQ}

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	2026-05-18T01:12:39.826285Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aac3b9cd27c096995a52352d0e28918c164b3c78e6a32fde3327f000f895eee1

Aliases

arxiv: 1606.02874 · arxiv_version: 1606.02874v1 · doi: 10.48550/arxiv.1606.02874 · pith_short_12: VLB3TTJHYCLJ · pith_short_16: VLB3TTJHYCLJSWSS · pith_short_8: VLB3TTJH

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/VLB3TTJHYCLJSWSSGUWQ4KERRQ \
  | 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: aac3b9cd27c096995a52352d0e28918c164b3c78e6a32fde3327f000f895eee1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3839716fe18c34f5e2eb5495638c7571175a94a58f49fb5a17c6d73d4c51adb5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-06-09T09:00:19Z",
    "title_canon_sha256": "3b39a60cf5c2ae6e9ec6c44ebf4ce10279c448406ac92eca2b9a722df11e835b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.02874",
    "kind": "arxiv",
    "version": 1
  }
}