Pith Number

pith:XZAG6TTP

pith:2011:XZAG6TTPVDPMLX6ZXAIOHQ7K3Z

not attested not anchored not stored refs pending

Shadowing and Expansivity in Sub-Spaces

Andrew Barwell, Chris Good, Piotr Oprocha

arxiv:1111.2812 v2 · 2011-11-11 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XZAG6TTPVDPMLX6ZXAIOHQ7K3Z}

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	2026-05-18T02:04:11.717373Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be406f4e6fa8dec5dfd9b810e3c3eade5abbf7b61a18a3c9f2bf148865c8da01

Aliases

arxiv: 1111.2812 · arxiv_version: 1111.2812v2 · doi: 10.48550/arxiv.1111.2812 · pith_short_12: XZAG6TTPVDPM · pith_short_16: XZAG6TTPVDPMLX6Z · pith_short_8: XZAG6TTP

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/XZAG6TTPVDPMLX6ZXAIOHQ7K3Z \
  | 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: be406f4e6fa8dec5dfd9b810e3c3eade5abbf7b61a18a3c9f2bf148865c8da01

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "914270a8a6a6ee6721eb78b6503d3508e88060828ff7a6758b91468768936ff7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-11-11T18:00:49Z",
    "title_canon_sha256": "6795af3a3d61cb0c4645844144ed09ab6d7f2e2b7f3b885e4913d6d9e6ffffed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.2812",
    "kind": "arxiv",
    "version": 2
  }
}