Pith Number

pith:TSVBZWTY

pith:2015:TSVBZWTYCTO66DVG56RUKQOMHZ

not attested not anchored not stored refs pending

On Ding injective, Ding projective, and Ding flat modules and complexes

James Gillespie

arxiv:1512.05999 v1 · 2015-12-18 · 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{TSVBZWTYCTO66DVG56RUKQOMHZ}

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	2026-05-18T01:24:05.681856Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9caa1cda7814ddef0ea6efa34541cc3e7e426bc591a5cb7e6a58fe05073efd16

Aliases

arxiv: 1512.05999 · arxiv_version: 1512.05999v1 · doi: 10.48550/arxiv.1512.05999 · pith_short_12: TSVBZWTYCTO6 · pith_short_16: TSVBZWTYCTO66DVG · pith_short_8: TSVBZWTY

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/TSVBZWTYCTO66DVG56RUKQOMHZ \
  | 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: 9caa1cda7814ddef0ea6efa34541cc3e7e426bc591a5cb7e6a58fe05073efd16

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd70ee2cd2197e4a35ddc988ca3895d1e8882aa6cdaac15ec9cac76947571009",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2015-12-18T15:45:34Z",
    "title_canon_sha256": "aff52f298b239fc915e3c64612bceea6a8f3604e01060d9fa60d4f6a04d17e48"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.05999",
    "kind": "arxiv",
    "version": 1
  }
}