Pith Number

pith:JMBDDNP7

pith:2024:JMBDDNP7UNE32Z2NUUWM6BERQN

not attested not anchored not stored refs pending

On Proving Ramanujan's Inequality using a Sharper Bound for the Prime Counting Function $\pi(x)$

Subham De

arxiv:2408.02591 v3 · 2024-08-05 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JMBDDNP7UNE32Z2NUUWM6BERQN}

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	2026-07-05T09:00:38.416324Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b0231b5ffa349bd674da52ccf04918371a70cb557aee82c01ea43a207b5b8ce

Aliases

arxiv: 2408.02591 · arxiv_version: 2408.02591v3 · doi: 10.48550/arxiv.2408.02591 · pith_short_12: JMBDDNP7UNE3 · pith_short_16: JMBDDNP7UNE32Z2N · pith_short_8: JMBDDNP7

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/JMBDDNP7UNE32Z2NUUWM6BERQN \
  | 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: 4b0231b5ffa349bd674da52ccf04918371a70cb557aee82c01ea43a207b5b8ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33ce1944cb4d6c002c739347582898b0283b658be6480c65a479bde3f2e63eb2",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-08-05T16:04:12Z",
    "title_canon_sha256": "48ccddd1ca11468ef8d16e99b36fb578a1ec8af10d481b0caa76129e4bb7ce97"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2408.02591",
    "kind": "arxiv",
    "version": 3
  }
}