Pith Number

pith:J62LNU7X

pith:2010:J62LNU7XHP7DSAY7MGB6UKK3E3

not attested not anchored not stored refs pending

On sums of Ramanujan sums

Angel V Kumchev, Tsz Ho Chan

arxiv:1009.4432 v2 · 2010-09-22 · 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{J62LNU7XHP7DSAY7MGB6UKK3E3}

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	2026-05-18T02:45:56.203870Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4fb4b6d3f73bfe39031f6183ea295b26fda1209ea31a341ade71198fbad3f34d

Aliases

arxiv: 1009.4432 · arxiv_version: 1009.4432v2 · doi: 10.48550/arxiv.1009.4432 · pith_short_12: J62LNU7XHP7D · pith_short_16: J62LNU7XHP7DSAY7 · pith_short_8: J62LNU7X

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/J62LNU7XHP7DSAY7MGB6UKK3E3 \
  | 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: 4fb4b6d3f73bfe39031f6183ea295b26fda1209ea31a341ade71198fbad3f34d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7f32098dae31b1147bd510af2f83b3bd590fec05793c9716c48adab05a44e5d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-09-22T17:29:17Z",
    "title_canon_sha256": "bf957eb35a0fab226fd44beab5ea333190d486e9ac8ea43c66c31ea28989c54b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.4432",
    "kind": "arxiv",
    "version": 2
  }
}