Pith Number

pith:TFWRSTTY

pith:2014:TFWRSTTYBHCNWXPG72IXLEXZRT

not attested not anchored not stored refs pending

Large gaps in the image of the Euler's function

Paolo Leonetti

arxiv:1411.3014 v2 · 2014-11-11 · 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{TFWRSTTYBHCNWXPG72IXLEXZRT}

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	2026-05-18T01:31:03.633387Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

996d194e7809c4db5de6fe917592f98cfef588567affb3ac44b89be3286a5afc

Aliases

arxiv: 1411.3014 · arxiv_version: 1411.3014v2 · doi: 10.48550/arxiv.1411.3014 · pith_short_12: TFWRSTTYBHCN · pith_short_16: TFWRSTTYBHCNWXPG · pith_short_8: TFWRSTTY

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/TFWRSTTYBHCNWXPG72IXLEXZRT \
  | 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: 996d194e7809c4db5de6fe917592f98cfef588567affb3ac44b89be3286a5afc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d056166d13017f584bcd1bc40c7879aadb9de446d413751a95bf5bc1c317934e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-11-11T23:12:50Z",
    "title_canon_sha256": "92708d8304c8813452aa1ec06fead8015aec415fba3b26328d38f5c1b44b7410"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.3014",
    "kind": "arxiv",
    "version": 2
  }
}