Pith Number

pith:GGRQKJIT

pith:2016:GGRQKJITBK632U6JP6G5L6PZK5

not attested not anchored not stored refs pending

Numerical modular symbols for elliptic curves

Christian Wuthrich

arxiv:1608.06423 v2 · 2016-08-23 · 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{GGRQKJITBK632U6JP6G5L6PZK5}

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	2026-05-18T00:48:05.518198Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31a30525130abdbd53c97f8dd5f9f95767ad9250fb49e4c2bd14ad634d9ecc11

Aliases

arxiv: 1608.06423 · arxiv_version: 1608.06423v2 · doi: 10.48550/arxiv.1608.06423 · pith_short_12: GGRQKJITBK63 · pith_short_16: GGRQKJITBK632U6J · pith_short_8: GGRQKJIT

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/GGRQKJITBK632U6JP6G5L6PZK5 \
  | 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: 31a30525130abdbd53c97f8dd5f9f95767ad9250fb49e4c2bd14ad634d9ecc11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e8a788304d46268227038d1addf8e7aa07b6f73d0cdd5338772d9e37c2818dd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-08-23T09:08:33Z",
    "title_canon_sha256": "eace10551e30f36d6bdbc13a6e2594a7fec05a153f2f5406dbc0f1569a88c54f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.06423",
    "kind": "arxiv",
    "version": 2
  }
}