Pith Number

pith:T5V6YPHW

pith:2024:T5V6YPHWLGHQ44O5SCN2ZHADBA

not attested not anchored not stored refs pending

Almost all elliptic curves with prescribed torsion have Szpiro ratio close to the expected value

Stephanie Chan

arxiv:2407.13850 v1 · 2024-07-18 · 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{T5V6YPHWLGHQ44O5SCN2ZHADBA}

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	2026-07-05T08:45:54.213741Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f6bec3cf6598f0e71dd909bac9c0308085f35c446ac4f216ef183fcf5a987b9

Aliases

arxiv: 2407.13850 · arxiv_version: 2407.13850v1 · doi: 10.48550/arxiv.2407.13850 · pith_short_12: T5V6YPHWLGHQ · pith_short_16: T5V6YPHWLGHQ44O5 · pith_short_8: T5V6YPHW

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/T5V6YPHWLGHQ44O5SCN2ZHADBA \
  | 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: 9f6bec3cf6598f0e71dd909bac9c0308085f35c446ac4f216ef183fcf5a987b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a24baf36097196664d393ea655dfeb61847405932b54703965e9cb990706e6b3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-07-18T18:34:24Z",
    "title_canon_sha256": "8a4cd889019d34bd9c75ef9b12ddc2fba4f9d9460e57cac2f6623b33d850c227"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2407.13850",
    "kind": "arxiv",
    "version": 1
  }
}