Pith Number

pith:7AXVMEK3

pith:2016:7AXVMEK3UAK4PDRS2ROTKWT7DE

not attested not anchored not stored refs pending

Directional derivatives and higher order chain rules for abelian functor calculus

Amelia Tebbe, Brenda Johnson, Christina Osborne, Emily Riehl, Kristine Bauer

arxiv:1610.01930 v2 · 2016-10-06 · math.AT · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7AXVMEK3UAK4PDRS2ROTKWT7DE}

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	2026-05-18T00:43:20.954869Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f82f56115ba015c78e32d45d355a7f19284490390488d7f710bf73135c306dc4

Aliases

arxiv: 1610.01930 · arxiv_version: 1610.01930v2 · doi: 10.48550/arxiv.1610.01930 · pith_short_12: 7AXVMEK3UAK4 · pith_short_16: 7AXVMEK3UAK4PDRS · pith_short_8: 7AXVMEK3

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/7AXVMEK3UAK4PDRS2ROTKWT7DE \
  | 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: f82f56115ba015c78e32d45d355a7f19284490390488d7f710bf73135c306dc4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "904bd18b74d5605c760f24ac355858f64a37bfd48d4266acc1853216f37346d5",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2016-10-06T16:16:49Z",
    "title_canon_sha256": "c236fd1961ca727a265ea853329af02cc24551910c8d169c20558cb6f646d7bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.01930",
    "kind": "arxiv",
    "version": 2
  }
}