Pith Number

pith:DTYLJD6O

pith:2019:DTYLJD6OWGNBKBKRZU377CRS4J

not attested not anchored not stored refs pending

Stability in graded rings associated with commutative augmented rings

Shan Chang

arxiv:1907.04579 v2 · 2019-07-10 · math.AC · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DTYLJD6OWGNBKBKRZU377CRS4J}

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	2026-07-05T00:28:50.228066Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1cf0b48fceb19a150551cd37ff8a32e262a775625775adad0f58d599d4557352

Aliases

arxiv: 1907.04579 · arxiv_version: 1907.04579v2 · doi: 10.48550/arxiv.1907.04579 · pith_short_12: DTYLJD6OWGNB · pith_short_16: DTYLJD6OWGNBKBKR · pith_short_8: DTYLJD6O

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/DTYLJD6OWGNBKBKRZU377CRS4J \
  | 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: 1cf0b48fceb19a150551cd37ff8a32e262a775625775adad0f58d599d4557352

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e589e1035cbbb2867f79c15a47aba2af45f8c29d5033f9d6de86a2f8a919c1ab",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2019-07-10T08:58:25Z",
    "title_canon_sha256": "6bac35ddd84ccdf086d65c8ad6f3971fca2d064f70e8784ae759841c1f464a2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.04579",
    "kind": "arxiv",
    "version": 2
  }
}