Pith Number

pith:NKNTIQZA

pith:2011:NKNTIQZA7FGUIQAFGXEPPRL3L6

not attested not anchored not stored refs pending

Polynomial maps with invertible sums of Jacobian matrices and of directional Derivatives

Hongbo Guo, Michiel de Bondt, Xiankun Du, Xiaosong Sun

arxiv:1106.0792 v1 · 2011-06-04 · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NKNTIQZA7FGUIQAFGXEPPRL3L6}

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	2026-05-18T03:09:23.228916Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a9b344320f94d44400535c8f7c57b5fb0d1c374ce8dbbfe2057dd997d923dc0

Aliases

arxiv: 1106.0792 · arxiv_version: 1106.0792v1 · doi: 10.48550/arxiv.1106.0792 · pith_short_12: NKNTIQZA7FGU · pith_short_16: NKNTIQZA7FGUIQAF · pith_short_8: NKNTIQZA

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/NKNTIQZA7FGUIQAFGXEPPRL3L6 \
  | 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: 6a9b344320f94d44400535c8f7c57b5fb0d1c374ce8dbbfe2057dd997d923dc0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa49fd8462a14300bb3131e519a3744514a0bef99a9263f8bc24f2c5f9d0e852",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-06-04T06:46:45Z",
    "title_canon_sha256": "62a241984680ad527a49bfcd75299f8a202046bfa31e947caef89c03e61aee28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.0792",
    "kind": "arxiv",
    "version": 1
  }
}