Pith Number

pith:IGPVRVQ5

pith:2011:IGPVRVQ5QVBHWKEYS7TEB7PATK

not attested not anchored not stored refs pending

Modified Growth Diagrams, Permutation Pivots, and the BXW map $\phi^*$

Dan Saracino, Jonathan Bloom

arxiv:1103.0319 v2 · 2011-03-02 · 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{IGPVRVQ5QVBHWKEYS7TEB7PATK}

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	2026-05-18T04:08:12.555012Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

419f58d61d85427b289897e640fde09abb921b1a022c574335d5e1997efee781

Aliases

arxiv: 1103.0319 · arxiv_version: 1103.0319v2 · doi: 10.48550/arxiv.1103.0319 · pith_short_12: IGPVRVQ5QVBH · pith_short_16: IGPVRVQ5QVBHWKEY · pith_short_8: IGPVRVQ5

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/IGPVRVQ5QVBHWKEYS7TEB7PATK \
  | 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: 419f58d61d85427b289897e640fde09abb921b1a022c574335d5e1997efee781

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6be493222c0eddfe7be99069658fd7ae7b4f2166fb7568bf4f1cd326d1e09c9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-03-02T00:03:56Z",
    "title_canon_sha256": "d95fc5845d585df1d376431140e76c4ab04da08b34f9bfcd7656ebb00370b00a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.0319",
    "kind": "arxiv",
    "version": 2
  }
}