Pith Number

pith:RV4Y27K7

pith:2019:RV4Y27K77F5VA5CIFPCFBVIRYM

not attested not anchored not stored refs pending

On the invariance of the string topology coproduct

Nathalie Wahl

arxiv:1908.03857 v4 · 2019-08-11 · math.AT · math.DG · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RV4Y27K77F5VA5CIFPCFBVIRYM}

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.

Cited by

1 paper in Pith

Poincar\'e duality for loop spaces

Receipt and verification

First computed	2026-07-05T08:56:53.547578Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8d798d7d5ff97b5074482bc450d511c331a72b1f7d5eb3889f2c57e6d4f3f5de

Aliases

arxiv: 1908.03857 · arxiv_version: 1908.03857v4 · doi: 10.48550/arxiv.1908.03857 · pith_short_12: RV4Y27K77F5V · pith_short_16: RV4Y27K77F5VA5CI · pith_short_8: RV4Y27K7

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/RV4Y27K77F5VA5CIFPCFBVIRYM \
  | 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: 8d798d7d5ff97b5074482bc450d511c331a72b1f7d5eb3889f2c57e6d4f3f5de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79220a4c12ae083a44df6b31aa1bc5a096923b8f7a4d0642d24e69a394482785",
    "cross_cats_sorted": [
      "math.DG",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2019-08-11T05:51:12Z",
    "title_canon_sha256": "2d1e5699065b62a2f6172535b49e097c20360fb8704543eb085c48489ce1b222"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.03857",
    "kind": "arxiv",
    "version": 4
  }
}