Pith Number

pith:HPJWFZKS

pith:2016:HPJWFZKSRESDBYZM5WPIUBFGRK

not attested not anchored not stored refs pending

On the theory of higher rank Euler, Kolyvagin and Stark systems

David Burns, Takamichi Sano

arxiv:1612.06187 v1 · 2016-12-19 · 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{HPJWFZKSRESDBYZM5WPIUBFGRK}

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	2026-05-18T00:54:42.944341Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3bd362e552892430e32ced9e8a04a68aac7f84f2d9d8cff7390dc719dd4501ba

Aliases

arxiv: 1612.06187 · arxiv_version: 1612.06187v1 · doi: 10.48550/arxiv.1612.06187 · pith_short_12: HPJWFZKSRESD · pith_short_16: HPJWFZKSRESDBYZM · pith_short_8: HPJWFZKS

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/HPJWFZKSRESDBYZM5WPIUBFGRK \
  | 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: 3bd362e552892430e32ced9e8a04a68aac7f84f2d9d8cff7390dc719dd4501ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "161ca944c0ef4d90ccd214ec2599c0838fecc9f5505bc441af1c4648c6bbb5df",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-12-19T14:10:09Z",
    "title_canon_sha256": "750ab1dd497193d68cbc1cbaccbd48b8331913affd42336b2828c11f8865cc08"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.06187",
    "kind": "arxiv",
    "version": 1
  }
}