Pith Number

pith:JQGFYUEJ

pith:2012:JQGFYUEJIQIGEDTTVIFK65UAMN

not attested not anchored not stored refs pending

On the representation of the number of integral points of an elliptic curve modulo a prime number

Michael Th. Rassias

arxiv:1210.1439 v3 · 2012-10-04 · 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{JQGFYUEJIQIGEDTTVIFK65UAMN}

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	2026-05-18T03:31:32.654445Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4c0c5c50894410620e73aa0aaf76806366a29e07189fa41b57d84bb1b596fb7a

Aliases

arxiv: 1210.1439 · arxiv_version: 1210.1439v3 · doi: 10.48550/arxiv.1210.1439 · pith_short_12: JQGFYUEJIQIG · pith_short_16: JQGFYUEJIQIGEDTT · pith_short_8: JQGFYUEJ

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/JQGFYUEJIQIGEDTTVIFK65UAMN \
  | 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: 4c0c5c50894410620e73aa0aaf76806366a29e07189fa41b57d84bb1b596fb7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b92d0611942243ca6e29f07b7cacf383c2c51e8bee993d0a9a510f69825c22d7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-10-04T13:47:15Z",
    "title_canon_sha256": "bd262ee2df1a5c08553c846585df6e0137998f21ab6a534b2f83f725027f2f6c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.1439",
    "kind": "arxiv",
    "version": 3
  }
}