Pith Number

pith:R7RRFSJQ

pith:2008:R7RRFSJQF2B5PU5MRXBVVIBSCV

not attested not anchored not stored refs pending

Concentration of the ratio between the geometric and arithmetic means

J. M. Aldaz

arxiv:0807.4832 v1 · 2008-07-30 · math.MG · 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{R7RRFSJQF2B5PU5MRXBVVIBSCV}

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	2026-05-18T04:39:08.311335Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8fe312c9302e83d7d3ac8dc35aa0321557342400f6f7b1f52306179cc15c7e3e

Aliases

arxiv: 0807.4832 · arxiv_version: 0807.4832v1 · doi: 10.48550/arxiv.0807.4832 · pith_short_12: R7RRFSJQF2B5 · pith_short_16: R7RRFSJQF2B5PU5M · pith_short_8: R7RRFSJQ

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/R7RRFSJQF2B5PU5MRXBVVIBSCV \
  | 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: 8fe312c9302e83d7d3ac8dc35aa0321557342400f6f7b1f52306179cc15c7e3e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af2861b1c39d49af3be4ff0ae6d3b52f798d9e2a87fa1479364cc8d45feea575",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2008-07-30T10:36:44Z",
    "title_canon_sha256": "3d3c4e66d2ef159340739de346a4db46b3eb508cb9353529b2a7bc6ec711e3c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0807.4832",
    "kind": "arxiv",
    "version": 1
  }
}