Pith Number

pith:HFMQVXV7

pith:2011:HFMQVXV72VYEM4UNDZTOACCNX4

not attested not anchored not stored refs pending

Sums of Ceiling Functions Solve Nested Recursions

Abraham Isgur, Rafal Drabek, Stephen Tanny, Vitaly Kuznetsov

arxiv:1107.3852 v1 · 2011-07-19 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HFMQVXV72VYEM4UNDZTOACCNX4}

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	2026-05-18T04:17:14.553124Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39590adebfd57046728d1e66e0084dbf3da5813c0b1c5177b3320514d0ffccc5

Aliases

arxiv: 1107.3852 · arxiv_version: 1107.3852v1 · doi: 10.48550/arxiv.1107.3852 · pith_short_12: HFMQVXV72VYE · pith_short_16: HFMQVXV72VYEM4UN · pith_short_8: HFMQVXV7

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/HFMQVXV72VYEM4UNDZTOACCNX4 \
  | 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: 39590adebfd57046728d1e66e0084dbf3da5813c0b1c5177b3320514d0ffccc5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe6c4fffe805bd7bac497003a403badbe54aba514903c58995bc35552555858b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-07-19T21:16:48Z",
    "title_canon_sha256": "f3e0fe79c1ff4da4a53224d28df253cfba974e2d26125ceb25567833d700a8b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.3852",
    "kind": "arxiv",
    "version": 1
  }
}