Pith Number

pith:ZOZKZ7Z4

pith:2012:ZOZKZ7Z4P244I6NMFXFJKHPRLE

not attested not anchored not stored refs pending

Milnor K-groups attached to elliptic curves over a p-adic field

Toshiro Hiranouchi

arxiv:1209.3208 v2 · 2012-09-14 · math.KT · 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{ZOZKZ7Z4P244I6NMFXFJKHPRLE}

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	2026-05-18T02:56:52.228110Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbb2acff3c7eb9c479ac2dca951df159108c4f54249abde9aba72b5f45451610

Aliases

arxiv: 1209.3208 · arxiv_version: 1209.3208v2 · doi: 10.48550/arxiv.1209.3208 · pith_short_12: ZOZKZ7Z4P244 · pith_short_16: ZOZKZ7Z4P244I6NM · pith_short_8: ZOZKZ7Z4

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/ZOZKZ7Z4P244I6NMFXFJKHPRLE \
  | 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: cbb2acff3c7eb9c479ac2dca951df159108c4f54249abde9aba72b5f45451610

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f5bc61cad2c3dc6e800351fb0025d99696ebe509122a3bc954ac39201fee55c",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2012-09-14T14:53:21Z",
    "title_canon_sha256": "2a4d024f453cccc5e1a2d05d47621ca2e3a563ffb888ece0dba30f99155947ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3208",
    "kind": "arxiv",
    "version": 2
  }
}