Pith Number

pith:IKCD7WGA

pith:2015:IKCD7WGAVMCML5I4ZMJRHMGW7Z

not attested not anchored not stored refs pending

Properties of vector-valued submodules on the bidisk

Constanze Liaw, Kelly Bickel

arxiv:1506.02759 v1 · 2015-06-09 · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IKCD7WGAVMCML5I4ZMJRHMGW7Z}

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	2026-05-18T01:01:45.100448Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42843fd8c0ab04c5f51ccb1313b0d6fe7a7f086b263703610e2f72add7cb5b84

Aliases

arxiv: 1506.02759 · arxiv_version: 1506.02759v1 · doi: 10.48550/arxiv.1506.02759 · pith_short_12: IKCD7WGAVMCM · pith_short_16: IKCD7WGAVMCML5I4 · pith_short_8: IKCD7WGA

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/IKCD7WGAVMCML5I4ZMJRHMGW7Z \
  | 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: 42843fd8c0ab04c5f51ccb1313b0d6fe7a7f086b263703610e2f72add7cb5b84

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4094dc665050a8d562892f138157c547a8edb3c8038990b252040a348b561df",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2015-06-09T03:06:27Z",
    "title_canon_sha256": "b0e31a918758004b47727077c85a3013f279b4fd5c7f860721ab3e80bf3a573a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.02759",
    "kind": "arxiv",
    "version": 1
  }
}