Pith Number

pith:OKKOSENQ

pith:2026:OKKOSENQW6CAYACM5ANXF4FPOI

not attested not anchored not stored refs pending

Upper bounds for moments of analytic ranks of elliptic curves over number fields

Saahil Sharma, Tristan Phillips

arxiv:2607.15998 v1 · 2026-07-17 · 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{OKKOSENQW6CAYACM5ANXF4FPOI}

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	2026-07-20T02:19:24.859162Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7294e911b0b7840c004ce81b72f0af723557525ba8c8319546fcf2d686d0da62

Aliases

arxiv: 2607.15998 · arxiv_version: 2607.15998v1 · doi: 10.48550/arxiv.2607.15998 · pith_short_12: OKKOSENQW6CA · pith_short_16: OKKOSENQW6CAYACM · pith_short_8: OKKOSENQ

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/OKKOSENQW6CAYACM5ANXF4FPOI \
  | 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: 7294e911b0b7840c004ce81b72f0af723557525ba8c8319546fcf2d686d0da62

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b690d5cb5c9bfca8aee3c870b7406f7350db0e20cfbf7d11a70e33305e275db",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-17T14:32:21Z",
    "title_canon_sha256": "ce0cf16ba12c29b57a04a082734f7e6c8cc211fa315605d57e3b03dd63aafcc3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.15998",
    "kind": "arxiv",
    "version": 1
  }
}