Pith Number

pith:7V2MUCQK

pith:2025:7V2MUCQK2GVSEHPOCDQ7VNG2JE

not attested not anchored not stored refs pending

Affine AP-frames and Stationary Random Processes

Hern\'an Diego Centeno, Juan Miguel Medina

arxiv:2507.15090 v2 · 2025-07-20 · math.PR · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7V2MUCQK2GVSEHPOCDQ7VNG2JE}

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	2026-05-20T00:02:05.590712Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd74ca0a0ad1ab221dee10e1fab4da490c46fb7a93a57900962228a104c7f287

Aliases

arxiv: 2507.15090 · arxiv_version: 2507.15090v2 · doi: 10.48550/arxiv.2507.15090 · pith_short_12: 7V2MUCQK2GVS · pith_short_16: 7V2MUCQK2GVSEHPO · pith_short_8: 7V2MUCQK

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/7V2MUCQK2GVSEHPOCDQ7VNG2JE \
  | 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: fd74ca0a0ad1ab221dee10e1fab4da490c46fb7a93a57900962228a104c7f287

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c1b0de4329c46ed9fddd0437e93c8be76acb31953b3e63db50a7399c7b83d59c",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-07-20T19:02:39Z",
    "title_canon_sha256": "8876b299a781e86e003b10ea9c2eb99cfad372287178ffc9d0c6c83384ba5067"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.15090",
    "kind": "arxiv",
    "version": 2
  }
}