Pith Number

pith:7QDI42VX

pith:2012:7QDI42VXOSUAYZ6KQEC56X6JE4

not attested not anchored not stored refs pending

Double Dirichlet series and quantum unique ergodicity of weight 1/2 Eisenstein series

Morten S. Risager, Nicole Raulf, Yiannis N. Petridis

arxiv:1209.1894 v4 · 2012-09-10 · math.NT · math.SP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7QDI42VXOSUAYZ6KQEC56X6JE4}

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	2026-05-18T01:22:26.262610Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc068e6ab774a80c67ca8105df5fc927136330608758d84a8f58e1fc08fe7c0c

Aliases

arxiv: 1209.1894 · arxiv_version: 1209.1894v4 · doi: 10.48550/arxiv.1209.1894 · pith_short_12: 7QDI42VXOSUA · pith_short_16: 7QDI42VXOSUAYZ6K · pith_short_8: 7QDI42VX

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/7QDI42VXOSUAYZ6KQEC56X6JE4 \
  | 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: fc068e6ab774a80c67ca8105df5fc927136330608758d84a8f58e1fc08fe7c0c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c29e5944e1bdf899552521687f7f2f1ec8d274223c12172f83fdaba58344a8d5",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-09-10T07:34:03Z",
    "title_canon_sha256": "3db41dea8410fb20597ab7d729f5d3ec8a63001ca9b9f0a99ac402c60d79f359"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.1894",
    "kind": "arxiv",
    "version": 4
  }
}