Pith Number

pith:X4FQMI4C

pith:2013:X4FQMI4CPKQYZRQTQPAOBRS63O

not attested not anchored not stored refs pending

Eisenstein series on rank 2 hyperbolic Kac--Moody groups

Dongwen Liu, Kyu-Hwan Lee, Lisa Carbone

arxiv:1306.3280 v3 · 2013-06-14 · math.RT · hep-th · 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{X4FQMI4CPKQYZRQTQPAOBRS63O}

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	2026-05-18T01:37:21.798775Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf0b0623827aa18cc61383c0e0c65edbb26fa0b8645e53cc07422c4e06482e61

Aliases

arxiv: 1306.3280 · arxiv_version: 1306.3280v3 · doi: 10.48550/arxiv.1306.3280 · pith_short_12: X4FQMI4CPKQY · pith_short_16: X4FQMI4CPKQYZRQT · pith_short_8: X4FQMI4C

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/X4FQMI4CPKQYZRQTQPAOBRS63O \
  | 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: bf0b0623827aa18cc61383c0e0c65edbb26fa0b8645e53cc07422c4e06482e61

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea21c5d6bad0c04c0b5fead6545bfef3369e0e46248f3ff6f93147a48fab0a4b",
    "cross_cats_sorted": [
      "hep-th",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2013-06-14T02:22:16Z",
    "title_canon_sha256": "dc22aced9cad0cbd6d646b5d89b027991b138bb54b712dd5b97b3d3116fa8e4f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.3280",
    "kind": "arxiv",
    "version": 3
  }
}