Pith Number

pith:O5KI6AFU

pith:2011:O5KI6AFU6GGHOAXB73ASF7FLLC

not attested not anchored not stored refs pending

Cusp Eigenforms and the Hall Algebra of an Elliptic Curve

Dragos Fratila

arxiv:1109.4308 v1 · 2011-09-20 · math.RT · math.AG · 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{O5KI6AFU6GGHOAXB73ASF7FLLC}

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	2026-05-17T23:53:19.233364Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

77548f00b4f18c7702e1fec122fcab58a988cdfd8338930a62de24d01b56a8d3

Aliases

arxiv: 1109.4308 · arxiv_version: 1109.4308v1 · doi: 10.48550/arxiv.1109.4308 · pith_short_12: O5KI6AFU6GGH · pith_short_16: O5KI6AFU6GGHOAXB · pith_short_8: O5KI6AFU

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/O5KI6AFU6GGHOAXB73ASF7FLLC \
  | 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: 77548f00b4f18c7702e1fec122fcab58a988cdfd8338930a62de24d01b56a8d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be901273b3aac2394f29e4f0545813768d620da042122fa55438d1099f49177b",
    "cross_cats_sorted": [
      "math.AG",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2011-09-20T14:31:58Z",
    "title_canon_sha256": "8e83ee2c45a727f3c07d6faf48f3cf157b919f96f58c9f8cd4c188bb13a2db61"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.4308",
    "kind": "arxiv",
    "version": 1
  }
}