Pith Number

pith:SOPXIHVE

pith:2016:SOPXIHVEV6WVP2ELFY5SOBI6QI

not attested not anchored not stored refs pending

Homotopy theory with bornological coarse spaces

Alexander Engel, Ulrich Bunke

arxiv:1607.03657 v4 · 2016-07-13 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SOPXIHVEV6WVP2ELFY5SOBI6QI}

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

Coarse cone quotients

Receipt and verification

First computed	2026-07-05T00:57:59.831199Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

939f741ea4afad57e88b2e3b27051e822b7c94fdca4ac26261c35c45af6be268

Aliases

arxiv: 1607.03657 · arxiv_version: 1607.03657v4 · doi: 10.48550/arxiv.1607.03657 · pith_short_12: SOPXIHVEV6WV · pith_short_16: SOPXIHVEV6WVP2EL · pith_short_8: SOPXIHVE

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/SOPXIHVEV6WVP2ELFY5SOBI6QI \
  | 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: 939f741ea4afad57e88b2e3b27051e822b7c94fdca4ac26261c35c45af6be268

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab163b37188ccb4847c83d34ca28baa38c93b8c8fe0c2782595e7d72da4f84d3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2016-07-13T09:46:16Z",
    "title_canon_sha256": "5a8c100558df9a143e989cec3ea151eb885212082c1738393968183923f7cd1f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.03657",
    "kind": "arxiv",
    "version": 4
  }
}