Pith Number

pith:7SOPFPZY

pith:2015:7SOPFPZYACCHU7GXBRBDAEIREL

not attested not anchored not stored refs pending

Two Applications of Brouwer's Fixed Point Theorem: in Insurance and in Biology Models

Muhamed Borogovac

arxiv:1503.04704 v3 · 2015-03-09 · math.OC · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7SOPFPZYACCHU7GXBRBDAEIREL}

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	2026-05-18T01:20:59.236646Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc9cf2bf3800847a7cd70c4230111122d12aa70f7e19d702486c6940e65c095d

Aliases

arxiv: 1503.04704 · arxiv_version: 1503.04704v3 · doi: 10.48550/arxiv.1503.04704 · pith_short_12: 7SOPFPZYACCH · pith_short_16: 7SOPFPZYACCHU7GX · pith_short_8: 7SOPFPZY

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/7SOPFPZYACCHU7GXBRBDAEIREL \
  | 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: fc9cf2bf3800847a7cd70c4230111122d12aa70f7e19d702486c6940e65c095d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e973fe3c77abd1e8e06f4d1002b9f0a3720e03b04aa9359d150344e996df578",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2015-03-09T02:13:09Z",
    "title_canon_sha256": "8107418d9dda8ca9e4f5f95ae8992ff7845ee13b7f80cc0e69c6be9bc9706480"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.04704",
    "kind": "arxiv",
    "version": 3
  }
}