Pith Number

pith:W64Q56R6

pith:2007:W64Q56R6Y2E22KQ5VKCD5NQFPA

not attested not anchored not stored refs pending

Relations among modular points on elliptic curves

Alexandru Buium, Bjorn Poonen

arxiv:0706.0566 v1 · 2007-06-05 · 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{W64Q56R6Y2E22KQ5VKCD5NQFPA}

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	2026-05-18T00:47:34.269696Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7b90efa3ec689ad2a1daa843eb605783511d716db32103c567b9f6ce2221c65

Aliases

arxiv: 0706.0566 · arxiv_version: 0706.0566v1 · doi: 10.48550/arxiv.0706.0566 · pith_short_12: W64Q56R6Y2E2 · pith_short_16: W64Q56R6Y2E22KQ5 · pith_short_8: W64Q56R6

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/W64Q56R6Y2E22KQ5VKCD5NQFPA \
  | 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: b7b90efa3ec689ad2a1daa843eb605783511d716db32103c567b9f6ce2221c65

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c341f62e30e641d43df12281223445fe2bc3f92f98f21ae8323151e829347a0f",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2007-06-05T01:45:21Z",
    "title_canon_sha256": "3163970019c88cae97b235e86809b26546e9b8e2a36c1a27f627b8116322a0df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0706.0566",
    "kind": "arxiv",
    "version": 1
  }
}