Pith Number

pith:M2MLIK5E

pith:2026:M2MLIK5EXXCA4G7KBXCXD6TLSZ

not attested not anchored not stored refs pending

Fourier Representations of Spectral Densities in Long-Memory Processes

Valentin Vidril

arxiv:2605.20041 v1 · 2026-05-19 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M2MLIK5EXXCA4G7KBXCXD6TLSZ}

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	2026-05-20T02:05:59.862579Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6698b42ba4bdc40e1bea0dc571fa6b96495fc9b8bf2203d3a4449277b4044680

Aliases

arxiv: 2605.20041 · arxiv_version: 2605.20041v1 · doi: 10.48550/arxiv.2605.20041 · pith_short_12: M2MLIK5EXXCA · pith_short_16: M2MLIK5EXXCA4G7K · pith_short_8: M2MLIK5E

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/M2MLIK5EXXCA4G7KBXCXD6TLSZ \
  | 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: 6698b42ba4bdc40e1bea0dc571fa6b96495fc9b8bf2203d3a4449277b4044680

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dca12787e6bfc4d30b288e24a2f2e526d88900003d95ae478e1b7cc18412fb8e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-19T16:03:19Z",
    "title_canon_sha256": "ab0f1425121add0de96713cdc5a972760696b7927a88a0bdcbf18315a01b0102"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.20041",
    "kind": "arxiv",
    "version": 1
  }
}