Pith Number

pith:RGC7XCE4

pith:2015:RGC7XCE4VEOGV7IFE2BRJRSJ2N

not attested not anchored not stored refs pending

On Tate-Shafarevich groups of 1-motives over Galois extensions

Cristian D. Gonzalez-Aviles

arxiv:1509.01316 v3 · 2015-09-04 · 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{RGC7XCE4VEOGV7IFE2BRJRSJ2N}

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	2026-05-18T01:22:48.084437Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8985fb889ca91c6afd05268314c649d34bb75bf3456bdcfe612e8f3a78613153

Aliases

arxiv: 1509.01316 · arxiv_version: 1509.01316v3 · doi: 10.48550/arxiv.1509.01316 · pith_short_12: RGC7XCE4VEOG · pith_short_16: RGC7XCE4VEOGV7IF · pith_short_8: RGC7XCE4

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/RGC7XCE4VEOGV7IFE2BRJRSJ2N \
  | 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: 8985fb889ca91c6afd05268314c649d34bb75bf3456bdcfe612e8f3a78613153

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "27a922b348942100816858e19153eb475674af5a6b6a63a60ee43b17d3443adc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-09-04T00:48:23Z",
    "title_canon_sha256": "210e4e308e84f6c3fe7498055c2252590d19067b3c82401705389204eeb887e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.01316",
    "kind": "arxiv",
    "version": 3
  }
}