Pith Number

pith:EM4SIEH2

pith:2023:EM4SIEH26QJZNHCX5S3KO3RL6V

not attested not anchored not stored refs pending

On the monotonicity of left and right Riemann sums

Ludovick Bouthat

arxiv:2311.01208 v2 · 2023-11-02 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EM4SIEH26QJZNHCX5S3KO3RL6V}

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	2026-06-23T02:13:12.101565Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

23392410faf413969c57ecb6a76e2bf5558bce6403751206f6210139dee6ed17

Aliases

arxiv: 2311.01208 · arxiv_version: 2311.01208v2 · doi: 10.48550/arxiv.2311.01208 · pith_short_12: EM4SIEH26QJZ · pith_short_16: EM4SIEH26QJZNHCX · pith_short_8: EM4SIEH2

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/EM4SIEH26QJZNHCX5S3KO3RL6V \
  | 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: 23392410faf413969c57ecb6a76e2bf5558bce6403751206f6210139dee6ed17

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f44e663871c272adb1ec69c819b282de3856555ce968af4a5a824b4263796f3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2023-11-02T13:02:31Z",
    "title_canon_sha256": "e723f92416c2230865d7908f99837738ebe9254093566a7342fc8d607996ca5a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2311.01208",
    "kind": "arxiv",
    "version": 2
  }
}