Pith Number

pith:FONPLU3K

pith:2016:FONPLU3KLV4Y2GYPCS7TV6I3PH

not attested not anchored not stored refs pending

Vanishing of relative homology and depth of tensor products

Arash Sadeghi, Li Liang, Olgur Celikbas

arxiv:1608.07011 v3 · 2016-08-25 · 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{FONPLU3KLV4Y2GYPCS7TV6I3PH}

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	2026-05-18T00:51:53.201215Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b9af5d36a5d798d1b0f14bf3af91b79d57bc4285baf502c70ee9c69094ad3a9

Aliases

arxiv: 1608.07011 · arxiv_version: 1608.07011v3 · doi: 10.48550/arxiv.1608.07011 · pith_short_12: FONPLU3KLV4Y · pith_short_16: FONPLU3KLV4Y2GYP · pith_short_8: FONPLU3K

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/FONPLU3KLV4Y2GYPCS7TV6I3PH \
  | 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: 2b9af5d36a5d798d1b0f14bf3af91b79d57bc4285baf502c70ee9c69094ad3a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2decd56b0f155e6ce3cf882a126a8055b207ea9bf3609c6073a3aefe230dda11",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2016-08-25T03:50:46Z",
    "title_canon_sha256": "1e5027243fb299a73c1825afd6fdedd81de89945bd937f400dbca3ea66b5734e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.07011",
    "kind": "arxiv",
    "version": 3
  }
}