Pith Number

pith:VN6ETXKW

pith:2026:VN6ETXKWYVOTUMEFZSYOXLPOLR

not attested not anchored not stored refs resolved

A vector field induced de Rham-Hodge theory on manifolds

Zhe Su

Any vector field on a manifold induces its own de Rham-Hodge theory by defining a modified inner product on forms.

arxiv:2605.15643 v1 · 2026-05-15 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VN6ETXKWYVOTUMEFZSYOXLPOLR}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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.

Claims

C1strongest claim

We then establish the resulting de Rham-Hodge theory for closed manifolds and extend it to manifolds with boundary by imposing certain vector field induced boundary conditions.

C2weakest assumption

A given vector field on the manifold induces an isomorphism on the space of differential forms that can be used to define a new L2 inner product and the associated operators.

C3one line summary

A vector field on a compact oriented manifold is used to induce an isomorphism on forms, from which a new L2 inner product, codifferential, and Hodge Laplacian are defined, yielding a de Rham-Hodge theory on closed manifolds and with boundary conditions on manifolds with boundary.

References

23 extracted · 23 resolved · 1 Pith anchors

[1] Differential Geometry and its Applications30(2), 179–194 (2012) 2012

[2] Publications Math´ ematiques de l’IH´ES68, 175–186 (1988) 1988

[3] ACM Transactions on Graphics (TOG)22(1), 4–32 (2003) 2003

[4] In: S´ eminaire de Probabilit´ es XIX 1983/84: Proceedings, pp 1983

[5] Results in Mathematics79(5), 187 (2024) 2024

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:09.706778Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab7c49dd56c55d3a3085ccb0ebadee5c5b76eaa802ef56a48618f850091a182b

Aliases

arxiv: 2605.15643 · arxiv_version: 2605.15643v1 · doi: 10.48550/arxiv.2605.15643 · pith_short_12: VN6ETXKWYVOT · pith_short_16: VN6ETXKWYVOTUMEF · pith_short_8: VN6ETXKW

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/VN6ETXKWYVOTUMEFZSYOXLPOLR \
  | 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: ab7c49dd56c55d3a3085ccb0ebadee5c5b76eaa802ef56a48618f850091a182b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8559ff454d414588448b3a18f06d7761b805268ed85746ae030625fc70ad23f4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-05-15T05:48:32Z",
    "title_canon_sha256": "59abc1edd24177f7eccf3f6cb5a8a44470cb6cdaf8c94526f9fc3502b895b9f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15643",
    "kind": "arxiv",
    "version": 1
  }
}