{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:XTZTR4HQEWDKHRC7M2ZLAPQ37V","short_pith_number":"pith:XTZTR4HQ","canonical_record":{"source":{"id":"2606.21295","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-19T10:18:24Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"665b00a985a28e7ab35e52fd030a4f387203e64606f1c782cfc065189913ceb0","abstract_canon_sha256":"87f966361c461e177cfd88850393e13582a8ffb1003d2a2f429632413649fdca"},"schema_version":"1.0"},"canonical_sha256":"bcf338f0f02586a3c45f66b2b03e1bfd41199161d56ae7976fa96a89656299fd","source":{"kind":"arxiv","id":"2606.21295","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.21295","created_at":"2026-06-23T01:12:36Z"},{"alias_kind":"arxiv_version","alias_value":"2606.21295v1","created_at":"2026-06-23T01:12:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.21295","created_at":"2026-06-23T01:12:36Z"},{"alias_kind":"pith_short_12","alias_value":"XTZTR4HQEWDK","created_at":"2026-06-23T01:12:36Z"},{"alias_kind":"pith_short_16","alias_value":"XTZTR4HQEWDKHRC7","created_at":"2026-06-23T01:12:36Z"},{"alias_kind":"pith_short_8","alias_value":"XTZTR4HQ","created_at":"2026-06-23T01:12:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:XTZTR4HQEWDKHRC7M2ZLAPQ37V","target":"record","payload":{"canonical_record":{"source":{"id":"2606.21295","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-19T10:18:24Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"665b00a985a28e7ab35e52fd030a4f387203e64606f1c782cfc065189913ceb0","abstract_canon_sha256":"87f966361c461e177cfd88850393e13582a8ffb1003d2a2f429632413649fdca"},"schema_version":"1.0"},"canonical_sha256":"bcf338f0f02586a3c45f66b2b03e1bfd41199161d56ae7976fa96a89656299fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T01:12:36.291900Z","signature_b64":"SCdGdVsVEMDLKgbr19+UFzWHXwMu9HdUdOhT/DA6PpjABYbvjJzxh+vXymTBfr4e+CrZG9IoadUptrb/75LhBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcf338f0f02586a3c45f66b2b03e1bfd41199161d56ae7976fa96a89656299fd","last_reissued_at":"2026-06-23T01:12:36.291450Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T01:12:36.291450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.21295","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-23T01:12:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7LnCMOH3orLjhNvzKZH+FIKa1iXrjMANqPxS7fFpi24ZXdMm3ibQ1qlnwQQrveFl3vycNkrntAyFvvQdqFVECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T08:14:02.796131Z"},"content_sha256":"96551147cde60043f6c8823c3abfa35de1c623a3a4ab49441a5ff84c2cc83b78","schema_version":"1.0","event_id":"sha256:96551147cde60043f6c8823c3abfa35de1c623a3a4ab49441a5ff84c2cc83b78"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:XTZTR4HQEWDKHRC7M2ZLAPQ37V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological Neural Dynamics: A Neuron-wise Framework for Sequence Modeling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Borui Cai, Yao Zhao","submitted_at":"2026-06-19T10:18:24Z","abstract_excerpt":"Existing sequence models, including RNNs, LSTMs, continuous-time networks, and Transformers, share a common structural principle: layer-wise dynamics, where all neurons in the same layer co-evolve through a shared parameterized operator, leaving individual neurons no freedom to evolve independently. Yet in many complex dynamical systems, rich global behavior emerges precisely from locally evolving units interacting through structured connectivity. Inspired by this principle, we introduce Topological Neural Dynamics (TND), a sequence modeling framework that shifts computation from layer-wise to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21295","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.21295/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-23T01:12:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HSgxanUMmdARg2x75A2cJ2avbPgFiIZ+COqL/r5fkh2LSWRmkGcEKEQECm9tPOrNpgquxKV61Z6mh3AMCvu8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T08:14:02.796514Z"},"content_sha256":"22d13985d6c562d609fe6f4778b5ec774556189d6cff57d52cb7f5fccbc88cfe","schema_version":"1.0","event_id":"sha256:22d13985d6c562d609fe6f4778b5ec774556189d6cff57d52cb7f5fccbc88cfe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XTZTR4HQEWDKHRC7M2ZLAPQ37V/bundle.json","state_url":"https://pith.science/pith/XTZTR4HQEWDKHRC7M2ZLAPQ37V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XTZTR4HQEWDKHRC7M2ZLAPQ37V/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-02T08:14:02Z","links":{"resolver":"https://pith.science/pith/XTZTR4HQEWDKHRC7M2ZLAPQ37V","bundle":"https://pith.science/pith/XTZTR4HQEWDKHRC7M2ZLAPQ37V/bundle.json","state":"https://pith.science/pith/XTZTR4HQEWDKHRC7M2ZLAPQ37V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XTZTR4HQEWDKHRC7M2ZLAPQ37V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XTZTR4HQEWDKHRC7M2ZLAPQ37V","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"87f966361c461e177cfd88850393e13582a8ffb1003d2a2f429632413649fdca","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-19T10:18:24Z","title_canon_sha256":"665b00a985a28e7ab35e52fd030a4f387203e64606f1c782cfc065189913ceb0"},"schema_version":"1.0","source":{"id":"2606.21295","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.21295","created_at":"2026-06-23T01:12:36Z"},{"alias_kind":"arxiv_version","alias_value":"2606.21295v1","created_at":"2026-06-23T01:12:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.21295","created_at":"2026-06-23T01:12:36Z"},{"alias_kind":"pith_short_12","alias_value":"XTZTR4HQEWDK","created_at":"2026-06-23T01:12:36Z"},{"alias_kind":"pith_short_16","alias_value":"XTZTR4HQEWDKHRC7","created_at":"2026-06-23T01:12:36Z"},{"alias_kind":"pith_short_8","alias_value":"XTZTR4HQ","created_at":"2026-06-23T01:12:36Z"}],"graph_snapshots":[{"event_id":"sha256:22d13985d6c562d609fe6f4778b5ec774556189d6cff57d52cb7f5fccbc88cfe","target":"graph","created_at":"2026-06-23T01:12:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.21295/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Existing sequence models, including RNNs, LSTMs, continuous-time networks, and Transformers, share a common structural principle: layer-wise dynamics, where all neurons in the same layer co-evolve through a shared parameterized operator, leaving individual neurons no freedom to evolve independently. Yet in many complex dynamical systems, rich global behavior emerges precisely from locally evolving units interacting through structured connectivity. Inspired by this principle, we introduce Topological Neural Dynamics (TND), a sequence modeling framework that shifts computation from layer-wise to","authors_text":"Borui Cai, Yao Zhao","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-19T10:18:24Z","title":"Topological Neural Dynamics: A Neuron-wise Framework for Sequence Modeling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21295","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:96551147cde60043f6c8823c3abfa35de1c623a3a4ab49441a5ff84c2cc83b78","target":"record","created_at":"2026-06-23T01:12:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"87f966361c461e177cfd88850393e13582a8ffb1003d2a2f429632413649fdca","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-19T10:18:24Z","title_canon_sha256":"665b00a985a28e7ab35e52fd030a4f387203e64606f1c782cfc065189913ceb0"},"schema_version":"1.0","source":{"id":"2606.21295","kind":"arxiv","version":1}},"canonical_sha256":"bcf338f0f02586a3c45f66b2b03e1bfd41199161d56ae7976fa96a89656299fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcf338f0f02586a3c45f66b2b03e1bfd41199161d56ae7976fa96a89656299fd","first_computed_at":"2026-06-23T01:12:36.291450Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T01:12:36.291450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SCdGdVsVEMDLKgbr19+UFzWHXwMu9HdUdOhT/DA6PpjABYbvjJzxh+vXymTBfr4e+CrZG9IoadUptrb/75LhBA==","signature_status":"signed_v1","signed_at":"2026-06-23T01:12:36.291900Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.21295","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96551147cde60043f6c8823c3abfa35de1c623a3a4ab49441a5ff84c2cc83b78","sha256:22d13985d6c562d609fe6f4778b5ec774556189d6cff57d52cb7f5fccbc88cfe"],"state_sha256":"03ee83e896a753d9513b70cd2b6515776a3fb4b29aa881aea90f3d2665986301"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IIQGzRH2n2bNwMZ5KL9vHtlhITaw165uMyc0Ymn9Aya7Peev9CGlcjyvKJdZHDU4XtG862gmABDgi5DVwy9yBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T08:14:02.798541Z","bundle_sha256":"8bc895e4284ef3b18cfcd4e30c396712f98cfff3b175a401b888b6a1aaa3d0cf"}}