Pith Number

pith:4GPRFAX5

pith:2018:4GPRFAX5NQARSINXZGFP6V6TPM

not attested not anchored not stored refs pending

Nearly hyperharmonic functions are infima of excessive functions

Ivan Netuka, Wolfhard Hansen

arxiv:1809.08611 v3 · 2018-09-23 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4GPRFAX5NQARSINXZGFP6V6TPM}

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	2026-05-17T23:44:07.625256Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e19f1282fd6c011921b7c98aff57d37b344ae50cc3615a7faf8c2c5dda69d98c

Aliases

arxiv: 1809.08611 · arxiv_version: 1809.08611v3 · doi: 10.48550/arxiv.1809.08611 · pith_short_12: 4GPRFAX5NQAR · pith_short_16: 4GPRFAX5NQARSINX · pith_short_8: 4GPRFAX5

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/4GPRFAX5NQARSINXZGFP6V6TPM \
  | 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: e19f1282fd6c011921b7c98aff57d37b344ae50cc3615a7faf8c2c5dda69d98c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5b08c52dff9b46327f7d9e3e3b0e9d3102f7efdcae3c53ed74d7db11cd14c42",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-09-23T15:04:04Z",
    "title_canon_sha256": "a702f90f61fe9ee2918ec816bb9c9cbd82c2c333621b8f8925beb516d8ab7720"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.08611",
    "kind": "arxiv",
    "version": 3
  }
}