Pith Number

pith:5P7PZN6P

pith:2009:5P7PZN6PDPGBBDNRFTUNMF6AS6

not attested not anchored not stored refs pending

On the reduction of points on abelian varieties and tori

Antonella Perucca

arxiv:0909.4806 v1 · 2009-09-25 · 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{5P7PZN6PDPGBBDNRFTUNMF6AS6}

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	2026-07-04T15:51:59.265007Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebfefcb7cf1bcc108db12ce8d617c097b5b47460f839e54e157b467507f853a7

Aliases

arxiv: 0909.4806 · arxiv_version: 0909.4806v1 · doi: 10.48550/arxiv.0909.4806 · pith_short_12: 5P7PZN6PDPGB · pith_short_16: 5P7PZN6PDPGBBDNR · pith_short_8: 5P7PZN6P

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/5P7PZN6PDPGBBDNRFTUNMF6AS6 \
  | 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: ebfefcb7cf1bcc108db12ce8d617c097b5b47460f839e54e157b467507f853a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40224e3dc8e86db7f47b0ecb81ddf7ee85fa61c00dd195c49291daf07dbe80e3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-09-25T21:22:31Z",
    "title_canon_sha256": "4fd6200fdc8d02b2092bf2d20b9f0c0f651dd696b35f349d0f7c9672fbf85eda"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.4806",
    "kind": "arxiv",
    "version": 1
  }
}