Pith Number

pith:F4ZPFCEQ

pith:2017:F4ZPFCEQ4MX36E5UVYPC6T5KH7

not attested not anchored not stored refs pending

Modular periodicity of the Euler numbers and a sequence by Arnold

Sanjay Ramassamy

arxiv:1712.08666 v1 · 2017-12-22 · math.CO · 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{F4ZPFCEQ4MX36E5UVYPC6T5KH7}

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	2026-05-18T00:16:44.491084Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f32f28890e32fbf13b4ae1e2f4faa3fdb27fd03411dd97ea5035b2cf7c0b481

Aliases

arxiv: 1712.08666 · arxiv_version: 1712.08666v1 · doi: 10.48550/arxiv.1712.08666 · pith_short_12: F4ZPFCEQ4MX3 · pith_short_16: F4ZPFCEQ4MX36E5U · pith_short_8: F4ZPFCEQ

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/F4ZPFCEQ4MX36E5UVYPC6T5KH7 \
  | 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: 2f32f28890e32fbf13b4ae1e2f4faa3fdb27fd03411dd97ea5035b2cf7c0b481

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "072cc61c6cd67085d4b42b44300d2f5575ed9cf726ec1303d6c390a1c48d25e1",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-12-22T21:26:37Z",
    "title_canon_sha256": "f53b9fcff71f9a03dfaa20a718b1147f3a3c6d2709acb6d1086dfd1bbd0792a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.08666",
    "kind": "arxiv",
    "version": 1
  }
}