{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:FG37P7LMPPSIWHDPTXVHUBSTLB","short_pith_number":"pith:FG37P7LM","canonical_record":{"source":{"id":"2606.24650","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-05-30T07:39:01Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"3d5f055ef7b3275c564002b1b81fff1476588a20caf6d7c661433b07c1da71db","abstract_canon_sha256":"09c9bc054f10bf2036d4a547f03e988806e93fd60af01734953dcc9bfab743d3"},"schema_version":"1.0"},"canonical_sha256":"29b7f7fd6c7be48b1c6f9dea7a0653586db045ddcede659c267873b3dde8db93","source":{"kind":"arxiv","id":"2606.24650","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.24650","created_at":"2026-06-24T01:15:38Z"},{"alias_kind":"arxiv_version","alias_value":"2606.24650v1","created_at":"2026-06-24T01:15:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.24650","created_at":"2026-06-24T01:15:38Z"},{"alias_kind":"pith_short_12","alias_value":"FG37P7LMPPSI","created_at":"2026-06-24T01:15:38Z"},{"alias_kind":"pith_short_16","alias_value":"FG37P7LMPPSIWHDP","created_at":"2026-06-24T01:15:38Z"},{"alias_kind":"pith_short_8","alias_value":"FG37P7LM","created_at":"2026-06-24T01:15:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:FG37P7LMPPSIWHDPTXVHUBSTLB","target":"record","payload":{"canonical_record":{"source":{"id":"2606.24650","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-05-30T07:39:01Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"3d5f055ef7b3275c564002b1b81fff1476588a20caf6d7c661433b07c1da71db","abstract_canon_sha256":"09c9bc054f10bf2036d4a547f03e988806e93fd60af01734953dcc9bfab743d3"},"schema_version":"1.0"},"canonical_sha256":"29b7f7fd6c7be48b1c6f9dea7a0653586db045ddcede659c267873b3dde8db93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T01:15:38.162429Z","signature_b64":"45BavtHoy+pToul6uKKVSih5KfEBLKI0EnRmjJZCwoQiMB8TTCVp0GAfyuncIFaR3AQ+xSk78aBesuHHVDW3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29b7f7fd6c7be48b1c6f9dea7a0653586db045ddcede659c267873b3dde8db93","last_reissued_at":"2026-06-24T01:15:38.162060Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T01:15:38.162060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.24650","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":"2026-06-24T01:15:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9eQzyW+5tCJmnapHKhzXxh6DZ/0hKvHFoczLQ+aQXgTn7v1ftBy4+LsGCtgXxO+KJ5MHSe1quDwof2Jk/UqHBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T19:24:29.877821Z"},"content_sha256":"aa24ef692023f98bbc06ffcfbfc044a2ed6edb6afe972040007cfc5d6f803a12","schema_version":"1.0","event_id":"sha256:aa24ef692023f98bbc06ffcfbfc044a2ed6edb6afe972040007cfc5d6f803a12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:FG37P7LMPPSIWHDPTXVHUBSTLB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Harmonic: Hierarchical State Space Models for Efficient Long-Context Language Modeling","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.CL","authors_text":"Petr Nyoma","submitted_at":"2026-05-30T07:39:01Z","abstract_excerpt":"We present Harmonic, a hierarchical state space model (SSM) for language modeling. The architecture stacks three recurrent levels at progressively slower timescales; each level receives the prediction error of the level below as input, rather than its raw hidden state. On enwiki8 with equal token budgets, Harmonic outperforms a comparable Transformer (28M params) by +1.4% at 1K tokens, +6.7% at 8K tokens, and +11.4% at 32K tokens (bpt, lower is better). It also outperforms Mamba at every tested length by 0.7--1.8%. At 64K tokens, both Mamba and Transformer run out of memory on an 80GB H100; Ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24650","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/2606.24650/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":"2026-06-24T01:15:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aIPaFZhoLEzn3jITS2PkaVjaqPvdi2HCoFBLH4ej28quuxdgnknjkUJmA8A8FTdkbBaC9Agr2wWsjXU7SOoYBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T19:24:29.878186Z"},"content_sha256":"83e78b228e398bfd1cc03a7c5423f095bcd9162b223611f4bf4c08c5172032ca","schema_version":"1.0","event_id":"sha256:83e78b228e398bfd1cc03a7c5423f095bcd9162b223611f4bf4c08c5172032ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FG37P7LMPPSIWHDPTXVHUBSTLB/bundle.json","state_url":"https://pith.science/pith/FG37P7LMPPSIWHDPTXVHUBSTLB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FG37P7LMPPSIWHDPTXVHUBSTLB/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":"2026-06-29T19:24:29Z","links":{"resolver":"https://pith.science/pith/FG37P7LMPPSIWHDPTXVHUBSTLB","bundle":"https://pith.science/pith/FG37P7LMPPSIWHDPTXVHUBSTLB/bundle.json","state":"https://pith.science/pith/FG37P7LMPPSIWHDPTXVHUBSTLB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FG37P7LMPPSIWHDPTXVHUBSTLB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FG37P7LMPPSIWHDPTXVHUBSTLB","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":"09c9bc054f10bf2036d4a547f03e988806e93fd60af01734953dcc9bfab743d3","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-05-30T07:39:01Z","title_canon_sha256":"3d5f055ef7b3275c564002b1b81fff1476588a20caf6d7c661433b07c1da71db"},"schema_version":"1.0","source":{"id":"2606.24650","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.24650","created_at":"2026-06-24T01:15:38Z"},{"alias_kind":"arxiv_version","alias_value":"2606.24650v1","created_at":"2026-06-24T01:15:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.24650","created_at":"2026-06-24T01:15:38Z"},{"alias_kind":"pith_short_12","alias_value":"FG37P7LMPPSI","created_at":"2026-06-24T01:15:38Z"},{"alias_kind":"pith_short_16","alias_value":"FG37P7LMPPSIWHDP","created_at":"2026-06-24T01:15:38Z"},{"alias_kind":"pith_short_8","alias_value":"FG37P7LM","created_at":"2026-06-24T01:15:38Z"}],"graph_snapshots":[{"event_id":"sha256:83e78b228e398bfd1cc03a7c5423f095bcd9162b223611f4bf4c08c5172032ca","target":"graph","created_at":"2026-06-24T01:15:38Z","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/2606.24650/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present Harmonic, a hierarchical state space model (SSM) for language modeling. The architecture stacks three recurrent levels at progressively slower timescales; each level receives the prediction error of the level below as input, rather than its raw hidden state. On enwiki8 with equal token budgets, Harmonic outperforms a comparable Transformer (28M params) by +1.4% at 1K tokens, +6.7% at 8K tokens, and +11.4% at 32K tokens (bpt, lower is better). It also outperforms Mamba at every tested length by 0.7--1.8%. At 64K tokens, both Mamba and Transformer run out of memory on an 80GB H100; Ha","authors_text":"Petr Nyoma","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-05-30T07:39:01Z","title":"Harmonic: Hierarchical State Space Models for Efficient Long-Context Language Modeling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24650","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:aa24ef692023f98bbc06ffcfbfc044a2ed6edb6afe972040007cfc5d6f803a12","target":"record","created_at":"2026-06-24T01:15:38Z","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":"09c9bc054f10bf2036d4a547f03e988806e93fd60af01734953dcc9bfab743d3","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-05-30T07:39:01Z","title_canon_sha256":"3d5f055ef7b3275c564002b1b81fff1476588a20caf6d7c661433b07c1da71db"},"schema_version":"1.0","source":{"id":"2606.24650","kind":"arxiv","version":1}},"canonical_sha256":"29b7f7fd6c7be48b1c6f9dea7a0653586db045ddcede659c267873b3dde8db93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29b7f7fd6c7be48b1c6f9dea7a0653586db045ddcede659c267873b3dde8db93","first_computed_at":"2026-06-24T01:15:38.162060Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T01:15:38.162060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"45BavtHoy+pToul6uKKVSih5KfEBLKI0EnRmjJZCwoQiMB8TTCVp0GAfyuncIFaR3AQ+xSk78aBesuHHVDW3Cw==","signature_status":"signed_v1","signed_at":"2026-06-24T01:15:38.162429Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.24650","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa24ef692023f98bbc06ffcfbfc044a2ed6edb6afe972040007cfc5d6f803a12","sha256:83e78b228e398bfd1cc03a7c5423f095bcd9162b223611f4bf4c08c5172032ca"],"state_sha256":"1f4215091b8e58ab9d86b8980075564ce83cb24e2380430c538083a75f1ee8f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kS2PaOlOzeiFIiGaH9+bPZPnxXWs0UDE5zT6Pa8w9GtsT4Nf0rVmQq8slwYORwVbWCyFqJw/MF5O5HTw/Nf/CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T19:24:29.880246Z","bundle_sha256":"d6bcfe027f2fbd055caeca8a1f1644a5f8911fa9bd69adebe7481ed42c8fecf3"}}