Pith Number

pith:6PARHDWS

pith:2021:6PARHDWSPCBR5CTQ2PYBKS6NOF

not attested not anchored not stored refs pending

Bernhard Riemann 1861 revisited: existence of flat coordinates for an arbitrary bilinear form

B. Dacorogna, M. Troyanov, S. Bandyopadhyay, V.S. Matveev

arxiv:2109.03098 v2 · 2021-09-07 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6PARHDWSPCBR5CTQ2PYBKS6NOF}

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	2026-07-05T07:20:05.107837Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3c1138ed278831e8a70d3f0154bcd7169f341de0fa7c9bdf9923f2086005ce1

Aliases

arxiv: 2109.03098 · arxiv_version: 2109.03098v2 · doi: 10.48550/arxiv.2109.03098 · pith_short_12: 6PARHDWSPCBR · pith_short_16: 6PARHDWSPCBR5CTQ · pith_short_8: 6PARHDWS

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/6PARHDWSPCBR5CTQ2PYBKS6NOF \
  | 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: f3c1138ed278831e8a70d3f0154bcd7169f341de0fa7c9bdf9923f2086005ce1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8efd8430a175608d7c6e1388b37ac17b63ee4444b99a070aaf5c77c0e4bec91d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2021-09-07T13:57:15Z",
    "title_canon_sha256": "b083983328842971fa80c406f7515ac0e5e982c7c7f3538c1cfbfded7fa5d671"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.03098",
    "kind": "arxiv",
    "version": 2
  }
}