Pith Number

pith:BA7M27OQ

pith:2026:BA7M27OQU23IB6LW7DZ66G3AY4

not attested not anchored not stored refs resolved

A Mathematical Characterization of Neural Activation Induced by Temporal Interference Stimulation

Antoine Chaillet, Esteban Paduro, Mario Sigalotti

Amplitudes and beat frequency together decide whether temporal interference stimulation leaves a neuron quiet, produces brief spikes, or drives continuous firing.

arxiv:2605.16761 v1 · 2026-05-16 · math.DS · q-bio.NC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BA7M27OQU23IB6LW7DZ66G3AY4}

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.

Claims

C1strongest claim

The amplitudes and beat frequency jointly determine whether the neuron remains quiescent, exhibits only transient responses, or undergoes persistent (tonic) firing.

C2weakest assumption

The FitzHugh-Nagumo equations, together with the geometric singular perturbation reduction, faithfully capture the activation thresholds of real neurons under the envelope produced by temporal interference stimulation (abstract, paragraph 3).

C3one line summary

Mathematical analysis of the FitzHugh-Nagumo model shows that TIS amplitudes and beat frequency jointly control whether a neuron remains quiescent, produces transient responses, or exhibits tonic firing.

References

29 extracted · 29 resolved · 0 Pith anchors

[1] Hoffman, and Suzanne J 1999 · doi:10.1016/s0005-

[2] E. Cerpa, N. Corrales, M. Courdurier, L. E. Medina, and E. Paduro. The Impact of High-Frequency-Based Stability on the Onset of Action Potentials in Neuron Models.SIAM Journal on Applied Mathematics, 1910 · doi:10.1137/24m1645632

[3] E. Cerpa, M. Courdurier, E. Hernández, L. E. Medina, and E. Paduro. A partially averaged system to model neuron responses to interferential current stimulation.J. Math. Biol., 86(1):8, 2023. doi:10.10 2023 · doi:10.1007/s00285-022-

[4] E.Cerpa, M.Courdurier, E.Hernández, L.E.Medina, andE.Paduro. Approximationandstabilityresultsfor the parabolic FitzHugh-Nagumo system with combined rapidly oscillating sources.Discrete and Continuous 2025 · doi:10.3934/dcds.2026001

[5] N. Grossman, D. Bono, N. Dedic, S. B. Kodandaramaiah, A. Rudenko, H.-J. Suk, A. M. Cassara, E. Neufeld, N. Kuster, L.-H. Tsai, A. Pascual-Leone, and E. S. Boyden. Noninvasive Deep Brain Stimulation vi 2017 · doi:10.1016/j.cell.2017.05.024

Receipt and verification

First computed	2026-05-20T00:03:20.428496Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

083ecd7dd0a6b680f976f8f3ef1b60c73afe24b5dff5efdf3070b2d835f1a62c

Aliases

arxiv: 2605.16761 · arxiv_version: 2605.16761v1 · doi: 10.48550/arxiv.2605.16761 · pith_short_12: BA7M27OQU23I · pith_short_16: BA7M27OQU23IB6LW · pith_short_8: BA7M27OQ

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/BA7M27OQU23IB6LW7DZ66G3AY4 \
  | 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: 083ecd7dd0a6b680f976f8f3ef1b60c73afe24b5dff5efdf3070b2d835f1a62c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "331f53e5819db1ffbd41f2ae44580daf896649108d28bb2140be1b07654bae00",
    "cross_cats_sorted": [
      "q-bio.NC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-16T02:18:51Z",
    "title_canon_sha256": "0a0bc34887fd73dc88dccd590120a8c062e4d7a91a5f8c209c6dc70f78905962"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16761",
    "kind": "arxiv",
    "version": 1
  }
}