Pith Number

pith:NAVPA2LS

pith:2017:NAVPA2LSAF67TWYE3Q4OXPGPER

not attested not anchored not stored refs pending

Sequences of Consecutive Happy Numbers in Negative Bases

Helen G. Grundman, Pamela E. Harris

arxiv:1705.04648 v1 · 2017-05-12 · 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{NAVPA2LSAF67TWYE3Q4OXPGPER}

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	2026-05-18T00:44:37.574434Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

682af06972017df9db04dc38ebbccf24654645c2ed397b20daa4e9e82db03a97

Aliases

arxiv: 1705.04648 · arxiv_version: 1705.04648v1 · doi: 10.48550/arxiv.1705.04648 · pith_short_12: NAVPA2LSAF67 · pith_short_16: NAVPA2LSAF67TWYE · pith_short_8: NAVPA2LS

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/NAVPA2LSAF67TWYE3Q4OXPGPER \
  | 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: 682af06972017df9db04dc38ebbccf24654645c2ed397b20daa4e9e82db03a97

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8654064844550705b8eeffa098ac75e8bf0945988f685ca4ec848d0df7a123eb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-05-12T16:39:52Z",
    "title_canon_sha256": "928c6d7c549b563bef4183b65b9219080b711ff0f222f76e9f124962ff7eeabe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.04648",
    "kind": "arxiv",
    "version": 1
  }
}