Pith Number

pith:NTA7LZ2V

pith:2016:NTA7LZ2VXDJJXYHRTFUPLW7Z5J

not attested not anchored not stored refs pending

A Bochner Formula for Harmonic Maps into Non-Positively Curved Metric Spaces

Brian Freidin

arxiv:1605.08461 v2 · 2016-05-26 · math.DG · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NTA7LZ2VXDJJXYHRTFUPLW7Z5J}

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	2026-05-18T00:30:17.650122Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6cc1f5e755b8d29be0f19968f5dbf9ea64f92bbaaee010a42e04b6664687bd22

Aliases

arxiv: 1605.08461 · arxiv_version: 1605.08461v2 · doi: 10.48550/arxiv.1605.08461 · pith_short_12: NTA7LZ2VXDJJ · pith_short_16: NTA7LZ2VXDJJXYHR · pith_short_8: NTA7LZ2V

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/NTA7LZ2VXDJJXYHRTFUPLW7Z5J \
  | 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: 6cc1f5e755b8d29be0f19968f5dbf9ea64f92bbaaee010a42e04b6664687bd22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "299ea511cbd0cc8c8dc522eabae6dfb25e255db6fd7fb548a790835ac88e77a6",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-05-26T22:00:46Z",
    "title_canon_sha256": "02a9819fafcc04a085fddd1c1b0f2f536085a0c1ec48615bda829c8ac2c4e40a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.08461",
    "kind": "arxiv",
    "version": 2
  }
}