Pith Number

pith:PHMN3VV3

pith:2014:PHMN3VV3YB5US5O45AGBTZAUDW

not attested not anchored not stored refs pending

An asymptotic for the average number of amicable pairs for elliptic curves

James Parks

arxiv:1410.5888 v2 · 2014-10-22 · 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{PHMN3VV3YB5US5O45AGBTZAUDW}

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	2026-05-18T01:22:08.448446Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79d8ddd6bbc07b4975dce80c19e4141daa863aca7a0de77eecb7ae545d2cae16

Aliases

arxiv: 1410.5888 · arxiv_version: 1410.5888v2 · doi: 10.48550/arxiv.1410.5888 · pith_short_12: PHMN3VV3YB5U · pith_short_16: PHMN3VV3YB5US5O4 · pith_short_8: PHMN3VV3

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/PHMN3VV3YB5US5O45AGBTZAUDW \
  | 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: 79d8ddd6bbc07b4975dce80c19e4141daa863aca7a0de77eecb7ae545d2cae16

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fdf7219878bbba4850feaac40773ba639a97781f2f3cc2cad1fa70ae1ca53209",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-10-22T00:10:33Z",
    "title_canon_sha256": "d8522c2ff712d7434847e10c7f865d2f32c4184d799e6dcde9e4dc5e93c64a6a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.5888",
    "kind": "arxiv",
    "version": 2
  }
}