Pith Number

pith:Z5B4UEW4

pith:2014:Z5B4UEW45KXL6BLFKLMD5DLQXV

not attested not anchored not stored refs pending

Stability of Frobenius direct images over surfaces

Congjun Liu, Mingshuo Zhou

arxiv:1407.6899 v1 · 2014-07-25 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z5B4UEW45KXL6BLFKLMD5DLQXV}

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	2026-05-18T02:46:32.070339Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf43ca12dceaaebf056552d83e8d70bd4c64939ecbbb9f9dfd298467ef89a721

Aliases

arxiv: 1407.6899 · arxiv_version: 1407.6899v1 · doi: 10.48550/arxiv.1407.6899 · pith_short_12: Z5B4UEW45KXL · pith_short_16: Z5B4UEW45KXL6BLF · pith_short_8: Z5B4UEW4

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/Z5B4UEW45KXL6BLFKLMD5DLQXV \
  | 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: cf43ca12dceaaebf056552d83e8d70bd4c64939ecbbb9f9dfd298467ef89a721

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1dbb6bf5968202dd745748d2955beeb7b504afc673bb74822d63fd80514ff37b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2014-07-25T13:57:45Z",
    "title_canon_sha256": "d168f9efc2236b1ced7feab5dea90b5d7c438cba5c89df81b1be8593a50bc464"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.6899",
    "kind": "arxiv",
    "version": 1
  }
}