Pith Number

pith:Q3GJZURB

pith:2010:Q3GJZURB52HZWCP4VBDCDE5Q34

not attested not anchored not stored refs pending

Implications of the Hasse Principle for Zero Cycles of Degree One on Principal Homogeneous Spaces

Jodi Black

arxiv:1010.1582 v1 · 2010-10-08 · 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{Q3GJZURB52HZWCP4VBDCDE5Q34}

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	2026-05-18T04:39:40.189977Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86cc9cd221ee8f9b09fca8462193b0df164df304f7695e78ab03544ae5ee9264

Aliases

arxiv: 1010.1582 · arxiv_version: 1010.1582v1 · doi: 10.48550/arxiv.1010.1582 · pith_short_12: Q3GJZURB52HZ · pith_short_16: Q3GJZURB52HZWCP4 · pith_short_8: Q3GJZURB

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/Q3GJZURB52HZWCP4VBDCDE5Q34 \
  | 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: 86cc9cd221ee8f9b09fca8462193b0df164df304f7695e78ab03544ae5ee9264

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f44ac564e9716018fd957f7ea57e228155cae7d3b155f915218c3c5faece6d4a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-10-08T01:59:27Z",
    "title_canon_sha256": "caa4ebc8e51ca026c4ae908ff9999df07156d8aa2f67a5e9cfb8ac15fb3074dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.1582",
    "kind": "arxiv",
    "version": 1
  }
}