Paper Citation Record · LEDGER

The Homological Brain: Parity Principle and Amortized Inference

As of 10 August 2026, this Paper Citation Record lists 57 of 57 outbound references and 1 inbound Pith citation observation for arXiv:2512.10976.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2512.10976 v2

Coverage vector

measured 57 of 57 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-17T02:54:11.747828Z

measured 58 of 58 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T15:02:50.255939Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

57 of 57 outbound references displayed

verified exact3
verified fuzzy54
unresolved0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 93988db4-05f3-45dd-802d-4ffb14bf2b7c · outbound

This paper cites 2002 Neuromorphic electronic systems.

The Homological Brain: Parity Principle and Amortized Inference 2002 Neuromorphic electronic systems

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T03:01:29.222441Z

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Observation 68383c57-d059-42b1-ab28-3b0ce0b2c7ae · outbound

This paper cites 2010 The free-energy principle: a uniﬁed brain theory?.

The Homological Brain: Parity Principle and Amortized Inference 2010 The free-energy principle: a uniﬁed brain theory?

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.220129Z

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Observation 24d1b364-81da-426a-8b35-ca14e0dae12c · outbound

This paper cites 2005Theoretical neuroscience: computational and mathematical modeling of neural systems.

The Homological Brain: Parity Principle and Amortized Inference 2005Theoretical neuroscience: computational and mathematical modeling of neural systems

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.282693Z

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Observation 6339950f-049e-4849-9455-081ff4b06f73 · outbound

This paper cites 1998 Perceptual neuroscience: the cerebral cortex.

The Homological Brain: Parity Principle and Amortized Inference 1998 Perceptual neuroscience: the cerebral cortex

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.267860Z

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Observation 59048a94-13ce-4fc0-9a4e-68cc32fb919d · outbound

This paper cites 1985 Learning internal representations by error propagation.

The Homological Brain: Parity Principle and Amortized Inference 1985 Learning internal representations by error propagation

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.270759Z

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Observation 158add78-2e06-4e20-a7f3-bba2fc010c07 · outbound

This paper cites 2014 Neuronal dynamics: From single neurons to networks and models of cognition.

The Homological Brain: Parity Principle and Amortized Inference 2014 Neuronal dynamics: From single neurons to networks and models of cognition

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.286007Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation fff81b50-d78c-4ede-bcb8-a8290d490a74 · outbound

This paper cites 2012 The economy of brain network organization.

The Homological Brain: Parity Principle and Amortized Inference 2012 The economy of brain network organization

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.295436Z

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Observation e9ba2fb2-35bf-4354-88a2-5c5fa5742fd9 · outbound

This paper cites 1949 The organization of behavior; a neuropsychological theory.

The Homological Brain: Parity Principle and Amortized Inference 1949 The organization of behavior; a neuropsychological theory

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.289406Z

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Observation 58fad2cd-9f0d-44a7-a259-34452e0c15b5 · outbound

This paper cites 2016 Information geometry and its applications vol.

The Homological Brain: Parity Principle and Amortized Inference 2016 Information geometry and its applications vol

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T03:01:29.240087Z

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Observation f7079364-57a3-44cd-9a2a-7213be2367ba · outbound

This paper cites 2012 Analog VLSI implementation of neural systems vol.

The Homological Brain: Parity Principle and Amortized Inference 2012 Analog VLSI implementation of neural systems vol

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T03:01:29.244442Z

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Observation 64bc70f3-7dfa-49c8-b3d5-6e9625a6549f · outbound

This paper cites 2025 Topological Neuroscience: Linking Circuits to Function.

The Homological Brain: Parity Principle and Amortized Inference 2025 Topological Neuroscience: Linking Circuits to Function

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T03:01:29.233788Z

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Observation e857d592-635e-44fc-ab78-b6b0ff11d289 · outbound

This paper cites 1990 Information, physics, quantum: The search for links.

The Homological Brain: Parity Principle and Amortized Inference 1990 Information, physics, quantum: The search for links

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T03:01:29.235984Z

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Observation 4222bafc-caaa-431d-a22d-6ee217128031 · outbound

This paper cites 2022 Computational topology: an introduction.

The Homological Brain: Parity Principle and Amortized Inference 2022 Computational topology: an introduction

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T03:01:29.246546Z

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Observation 60f6b752-95a3-40e6-86c6-da6903fbe528 · outbound

This paper cites 2014 Amortized inference in probabilistic reasoning.

The Homological Brain: Parity Principle and Amortized Inference 2014 Amortized inference in probabilistic reasoning

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T03:01:29.229430Z

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Observation 93339471-bb35-4a6d-9a78-36d3f6ba6d63 · outbound

This paper cites Relationships between nondeterministic and determin- istic tape complexities.

The Homological Brain: Parity Principle and Amortized Inference Relationships between nondeterministic and determin- istic tape complexities

Reference 15

Resolution: verified exact; doi, observed 2026-05-17T02:58:54.770071Z

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Observation dceffcfa-7a87-4d4d-af53-c0312dd1049f · outbound

This paper cites 1966 Dynamic programming.

The Homological Brain: Parity Principle and Amortized Inference 1966 Dynamic programming

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.337788Z

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Observation 94fbeed6-6e5e-47d9-9d8e-566fc323b918 · outbound

This paper cites 2013 The theta-gamma neural code.

The Homological Brain: Parity Principle and Amortized Inference 2013 The theta-gamma neural code

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.335161Z

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Observation 69399559-b7c7-4513-89e4-74512fb84f6b · outbound

This paper cites 2018 Geometry, topology and physics.

The Homological Brain: Parity Principle and Amortized Inference 2018 Geometry, topology and physics

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.340631Z

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Observation cbfc6139-70ea-4d74-9c14-f300f149fe45 · outbound

This paper cites 1929 The uncertainty principle.

The Homological Brain: Parity Principle and Amortized Inference 1929 The uncertainty principle

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T03:01:29.231542Z

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Observation 43ffbda0-f627-46c3-be44-ce147b5097da · outbound

This paper cites 2010 Colloquium: topological insulators.

The Homological Brain: Parity Principle and Amortized Inference 2010 Colloquium: topological insulators

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T03:01:29.238022Z

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Observation 415970de-d468-469e-ad57-c455c0b90e95 · outbound

This paper cites 1998 Elements of applied bifurcation theory.

The Homological Brain: Parity Principle and Amortized Inference 1998 Elements of applied bifurcation theory

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T03:01:29.242220Z

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Observation aa504793-c149-454c-8f42-2d0c51324f29 · outbound

This paper cites John Wiley & Sons.

The Homological Brain: Parity Principle and Amortized Inference John Wiley & Sons

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T03:01:29.224963Z

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Observation 89d3c747-1699-4516-9557-fa85b6a5f7c5 · outbound

This paper cites 2015 Memory consolidation.

The Homological Brain: Parity Principle and Amortized Inference 2015 Memory consolidation

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.320866Z

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Observation 6a0fd507-350a-4883-a1ef-4695e89953e1 · outbound

This paper cites 1967 Computation: Finite and Inﬁnite Machines.

The Homological Brain: Parity Principle and Amortized Inference 1967 Computation: Finite and Inﬁnite Machines

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.318264Z

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Observation b3418b48-66ad-4659-b568-89b601119137 · outbound

This paper cites 1957 Modality and topographic properties of single neurons of cat’s somatic sensory cortex.

The Homological Brain: Parity Principle and Amortized Inference 1957 Modality and topographic properties of single neurons of cat’s somatic sensory cortex

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.327237Z

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Observation 0866738a-2a99-4cab-80e6-7c0f36e342f6 · outbound

This paper cites 2008 Spike timing–dependent plasticity: a Hebbian learning rule.

The Homological Brain: Parity Principle and Amortized Inference 2008 Spike timing–dependent plasticity: a Hebbian learning rule

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.330103Z

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Observation 83760d76-40c4-4111-a228-05448b6715b4 · outbound

This paper cites 1996 The hippocampo-neocortical dialogue.

The Homological Brain: Parity Principle and Amortized Inference 1996 The hippocampo-neocortical dialogue

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.306959Z

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Observation 547e969f-b03b-42cb-af31-d6ce1ca0c7dc · outbound

This paper cites wake-sleep.

The Homological Brain: Parity Principle and Amortized Inference wake-sleep

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.309758Z

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Observation 300870aa-2ae4-4510-98ff-4c8aa3308561 · outbound

This paper cites 2011 Thinking, fast and slow.

The Homological Brain: Parity Principle and Amortized Inference 2011 Thinking, fast and slow

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.332604Z

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Observation f7190fa5-b122-40b9-87c2-0890e16bcf7f · outbound

This paper cites 2011 The Feynman lectures on physics, Vol.

The Homological Brain: Parity Principle and Amortized Inference 2011 The Feynman lectures on physics, Vol

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.315236Z

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Observation 02429feb-2d92-4986-8b44-f5f8d42aa9b3 · outbound

This paper cites 1972 Episodic and semantic memory.

The Homological Brain: Parity Principle and Amortized Inference 1972 Episodic and semantic memory

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T03:01:29.227098Z

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Observation 8b22a965-4783-48c9-9b07-c66b7dfea232 · outbound

This paper cites 2025 Principles of biological autonomy.

The Homological Brain: Parity Principle and Amortized Inference 2025 Principles of biological autonomy

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.273868Z

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Observation e54a06e9-66da-40b2-a73f-14a9497d2136 · outbound

This paper cites 1985 Does the autistic child have a theory of mind?.

The Homological Brain: Parity Principle and Amortized Inference 1985 Does the autistic child have a theory of mind?

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.261568Z

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Observation 323f66d3-33fc-4898-beff-35e0571a24a4 · outbound

This paper cites Sheaf theory: from deep geometry to deep learning.

The Homological Brain: Parity Principle and Amortized Inference Sheaf theory: from deep geometry to deep learning

Reference 34

Resolution: verified exact; arxiv_id, observed 2026-05-17T02:58:55.207093Z

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Observation 8a66f3e4-e211-4b24-97cd-8ac0d8e8b2da · outbound

This paper cites 2006 Polychronization: computation with spikes.

The Homological Brain: Parity Principle and Amortized Inference 2006 Polychronization: computation with spikes

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.256021Z

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Observation aa400427-04aa-4565-9552-e015e0b79114 · outbound

This paper cites 2005 Algebraic topology.

The Homological Brain: Parity Principle and Amortized Inference 2005 Algebraic topology

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.258752Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 74d8ab64-c466-4b35-afc6-58ba5000b9bf · outbound

This paper cites 1994 Reactivation of hippocampal ensemble memories during sleep.

The Homological Brain: Parity Principle and Amortized Inference 1994 Reactivation of hippocampal ensemble memories during sleep

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.264449Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d34957b8-434c-4bc5-b258-9a32e459ef72 · outbound

This paper cites 1961 Irreversibility and heat generation in the computing process.

The Homological Brain: Parity Principle and Amortized Inference 1961 Irreversibility and heat generation in the computing process

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.276890Z

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Observation 5c8bc2d1-39b6-4cb5-bc64-1800923ff2d8 · outbound

This paper cites 1997 The columnar organization of the neocortex.

The Homological Brain: Parity Principle and Amortized Inference 1997 The columnar organization of the neocortex

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.279681Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation ae7c0322-de51-4ea4-9518-35f4c473e5ab · outbound

This paper cites 2006 Rhythms of the Brain.

The Homological Brain: Parity Principle and Amortized Inference 2006 Rhythms of the Brain

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.292418Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 29348245-8728-46ff-a901-097f879e356e · outbound

This paper cites 1992 Q-learning.Machine learning 8, 279–292.

The Homological Brain: Parity Principle and Amortized Inference 1992 Q-learning.Machine learning 8, 279–292

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.244400Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 243edf0d-9e51-4e21-bfb6-62934619b5c1 · outbound

This paper cites 2018 Reinforcement learning: An introduction.

The Homological Brain: Parity Principle and Amortized Inference 2018 Reinforcement learning: An introduction

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.241607Z

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Observation af31c44b-89a5-48db-b54f-5ed1257b0274 · outbound

This paper cites 2005 New approaches to demystifying insight.

The Homological Brain: Parity Principle and Amortized Inference 2005 New approaches to demystifying insight

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.247296Z

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Observation ff765d0b-493f-4ebe-8270-835ce8dde464 · outbound

This paper cites 2008 A universe of consciousness: How matter becomes imagination.

The Homological Brain: Parity Principle and Amortized Inference 2008 A universe of consciousness: How matter becomes imagination

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.250231Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 54e1c4ca-a758-4e0e-8132-a54eec6cc55b · outbound

This paper cites 2016 Integrated information theory: from consciousness to its physical substrate.

The Homological Brain: Parity Principle and Amortized Inference 2016 Integrated information theory: from consciousness to its physical substrate

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.229147Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 5b423a17-42db-407e-b223-8cca73ff8a41 · outbound

This paper cites 2005 Theory of mind.

The Homological Brain: Parity Principle and Amortized Inference 2005 Theory of mind

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.235508Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1d6e71f9-9bc1-4b60-ad4c-ebb9579dab51 · outbound

This paper cites 2003Phenomenal consciousness: A naturalistic theory.

The Homological Brain: Parity Principle and Amortized Inference 2003Phenomenal consciousness: A naturalistic theory

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.232335Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation c47c1e11-a508-45e6-b824-fe0dca8cdff1 · outbound

This paper cites 1995 On a confusion about a function of consciousness.

The Homological Brain: Parity Principle and Amortized Inference 1995 On a confusion about a function of consciousness

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.226118Z

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Observation 30bc3bf5-dbb5-4c89-a6b6-9b4e865546e9 · outbound

This paper cites 2000 The paradox of self-consciousness.

The Homological Brain: Parity Principle and Amortized Inference 2000 The paradox of self-consciousness

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.223095Z

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Observation e783192c-fd85-4584-a63a-4b108769eba2 · outbound

This paper cites 2017 The hard problem of consciousness.

The Homological Brain: Parity Principle and Amortized Inference 2017 The hard problem of consciousness

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.238372Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3b81b7ab-74c2-486c-b2f2-81ba1355eae8 · outbound

This paper cites 1998 Epiphenomenal qualia.

The Homological Brain: Parity Principle and Amortized Inference 1998 Epiphenomenal qualia

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.252977Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 82cbaeb1-464d-407b-9ee5-a54238261dc0 · outbound

This paper cites Sparks of Artificial General Intelligence: Early experiments with GPT-4.

The Homological Brain: Parity Principle and Amortized Inference Sparks of Artificial General Intelligence: Early experiments with GPT-4

Reference 52

Resolution: verified exact; local_arxiv, observed 2026-05-17T02:58:55.202470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation cdc24b1c-2a2b-4238-8487-831673e9d761 · outbound

This paper cites 2004 Core mechanisms in theory of mind.

The Homological Brain: Parity Principle and Amortized Inference 2004 Core mechanisms in theory of mind

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.312644Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 90132b54-91d5-4bab-b3fc-94173f67b40d · outbound

This paper cites 2009 Imitation, empathy , and mirror neurons.

The Homological Brain: Parity Principle and Amortized Inference 2009 Imitation, empathy , and mirror neurons

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.323543Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 9a96970c-a2fa-4e54-a0dc-c5dd0f0a5ab7 · outbound

This paper cites 2016 Empathy: A review of the concept.

The Homological Brain: Parity Principle and Amortized Inference 2016 Empathy: A review of the concept

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.304303Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 17805c3f-c49c-4699-ae74-4d64a7f417da · outbound

This paper cites 2018 Affect regulation, mentalization and the development of the self.

The Homological Brain: Parity Principle and Amortized Inference 2018 Affect regulation, mentalization and the development of the self

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.301580Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation c7363aa2-07d9-4f8a-8ac0-0c8e16af4625 · outbound

This paper cites 1987 Social cognition and social perception.

The Homological Brain: Parity Principle and Amortized Inference 1987 Social cognition and social perception

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T02:58:56.298646Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Pith citing papers

Observation b9459fe4-d97c-4889-9256-2a51c17d8ec4 · inbound

The Urysohn Ladder: Recursive Metric Contraction for Scalable Continual Learning cites this paper.

The Urysohn Ladder: Recursive Metric Contraction for Scalable Continual Learning The Homological Brain: Parity Principle and Amortized Inference

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-03T15:02:50.255939Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.