Pith Number

pith:LGQZH6TD

pith:2015:LGQZH6TDA5SWNXAUZLHMJ46GNR

not attested not anchored not stored refs pending

Beyond Endoscopy via the trace formula - II: Asymptotic expansions of Fourier transforms and bounds towards the Ramanujan conjecture

Salim Ali Altug

arxiv:1506.08911 v2 · 2015-06-30 · math.NT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LGQZH6TDA5SWNXAUZLHMJ46GNR}

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	2026-05-18T01:23:33.477519Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

59a193fa63076566dc14cacec4f3c66c7dce5e8191ced856f373ab9420d5069a

Aliases

arxiv: 1506.08911 · arxiv_version: 1506.08911v2 · doi: 10.48550/arxiv.1506.08911 · pith_short_12: LGQZH6TDA5SW · pith_short_16: LGQZH6TDA5SWNXAU · pith_short_8: LGQZH6TD

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/LGQZH6TDA5SWNXAUZLHMJ46GNR \
  | 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: 59a193fa63076566dc14cacec4f3c66c7dce5e8191ced856f373ab9420d5069a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19cbd6a9545cddf7606a55ac2ebc44b3202944e65318e24056c1e2916603b8fc",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-06-30T00:52:44Z",
    "title_canon_sha256": "edc6ab2f233f86480a9095f033ef542272346f6322e0266260650da08356e162"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.08911",
    "kind": "arxiv",
    "version": 2
  }
}