Pith Number

pith:IGVGNITM

pith:2008:IGVGNITM5CQEJFWU4GOGJILVZN

not attested not anchored not stored refs pending

On some congruence properties of elliptic curves

Derong Qiu

arxiv:0803.2809 v5 · 2008-03-19 · math.NT · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IGVGNITM5CQEJFWU4GOGJILVZN}

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	2026-05-18T03:54:26.499147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

41aa66a26ce8a04496d4e19c64a175cb70a38b0370c007a2a6f32ef2eb0f0832

Aliases

arxiv: 0803.2809 · arxiv_version: 0803.2809v5 · doi: 10.48550/arxiv.0803.2809 · pith_short_12: IGVGNITM5CQE · pith_short_16: IGVGNITM5CQEJFWU · pith_short_8: IGVGNITM

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/IGVGNITM5CQEJFWU4GOGJILVZN \
  | 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: 41aa66a26ce8a04496d4e19c64a175cb70a38b0370c007a2a6f32ef2eb0f0832

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2da336bfa21f1956d6452added98d9fc3859dacccba334cff107ab58ca8c5f33",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2008-03-19T14:44:52Z",
    "title_canon_sha256": "32cc4cef237bf5dfc24590108238c0b926c7ca67248477ab440857a0e37f959f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0803.2809",
    "kind": "arxiv",
    "version": 5
  }
}