{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:MNAVZBSGYQG3BMNDVKBLQYKYZU","short_pith_number":"pith:MNAVZBSG","canonical_record":{"source":{"id":"1112.5491","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-12-22T23:37:28Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"21d30b9d98414c5378d41f1a8c058b2ed119fc4c8ee62f348919a27f7e856816","abstract_canon_sha256":"892026f13fb0d894156d135770542af4b9c85cc49ca17ce25f263c182a097393"},"schema_version":"1.0"},"canonical_sha256":"63415c8646c40db0b1a3aa82b86158cd2893c6911c32041f1a5491df360502c8","source":{"kind":"arxiv","id":"1112.5491","version":8},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.5491","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"arxiv_version","alias_value":"1112.5491v8","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5491","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"pith_short_12","alias_value":"MNAVZBSGYQG3","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MNAVZBSGYQG3BMND","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MNAVZBSG","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:MNAVZBSGYQG3BMNDVKBLQYKYZU","target":"record","payload":{"canonical_record":{"source":{"id":"1112.5491","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-12-22T23:37:28Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"21d30b9d98414c5378d41f1a8c058b2ed119fc4c8ee62f348919a27f7e856816","abstract_canon_sha256":"892026f13fb0d894156d135770542af4b9c85cc49ca17ce25f263c182a097393"},"schema_version":"1.0"},"canonical_sha256":"63415c8646c40db0b1a3aa82b86158cd2893c6911c32041f1a5491df360502c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:53.241070Z","signature_b64":"1Fm+sYMwkssf0gdepnPefOPhCgk49seW8z8NNviJug6pVy4x0azOOLlo8807sPi7U6Bkkcw6ks/ZWQPVuBlKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63415c8646c40db0b1a3aa82b86158cd2893c6911c32041f1a5491df360502c8","last_reissued_at":"2026-05-18T02:47:53.240530Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:53.240530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.5491","source_version":8,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jO8aluOB62Nemoo0PedsulVThfcC5XPIJwqp5ls5byR0Re8JOo1JnEnrC+3lxbIn6CQmOmuMme5TIh3ogR2kDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:05:53.191648Z"},"content_sha256":"ce17d3ecb2de36e242f9817148082fe744a5b89b45ec2eb1252d16ac025af5df","schema_version":"1.0","event_id":"sha256:ce17d3ecb2de36e242f9817148082fe744a5b89b45ec2eb1252d16ac025af5df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:MNAVZBSGYQG3BMNDVKBLQYKYZU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Time's Arrow for Shockwaves ; Bit-Reversible Lyapunov and \"Covariant\" Vectors ; Symmetry Breaking","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"cond-mat.stat-mech","authors_text":"Carol G. Hoover, Wm. G. Hoover","submitted_at":"2011-12-22T23:37:28Z","abstract_excerpt":"Strong shockwaves generate entropy quickly and locally. The Newton-Hamilton equations of motion, which underly the dynamics, are perfectly time-reversible. How do they generate the irreversible shock entropy? What are the symptoms of this irreversibility? We investigate these questions using Levesque and Verlet's bit-reversible algorithm. In this way we can generate an entirely imaginary past consistent with the irreversibility observed in the present. We use Runge-Kutta integration to analyze the local Lyapunov instability of the forward and backward processes so as to identify those particle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5491","kind":"arxiv","version":8},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T02:47:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VqjHW0s5gremy+QFnkBxbCEHPYo3GuXPwIrFe4JYqAFAqoipj3Fg3DBpoh6FFg7Yl2VGck/xrOuZmwURUlakAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:05:53.191993Z"},"content_sha256":"860a30f60eff7b8f260b9ebda30e4b4dd7f828c8592ed243d53adc9503998884","schema_version":"1.0","event_id":"sha256:860a30f60eff7b8f260b9ebda30e4b4dd7f828c8592ed243d53adc9503998884"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MNAVZBSGYQG3BMNDVKBLQYKYZU/bundle.json","state_url":"https://pith.science/pith/MNAVZBSGYQG3BMNDVKBLQYKYZU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MNAVZBSGYQG3BMNDVKBLQYKYZU/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":"2026-06-22T18:05:53Z","links":{"resolver":"https://pith.science/pith/MNAVZBSGYQG3BMNDVKBLQYKYZU","bundle":"https://pith.science/pith/MNAVZBSGYQG3BMNDVKBLQYKYZU/bundle.json","state":"https://pith.science/pith/MNAVZBSGYQG3BMNDVKBLQYKYZU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MNAVZBSGYQG3BMNDVKBLQYKYZU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MNAVZBSGYQG3BMNDVKBLQYKYZU","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":"892026f13fb0d894156d135770542af4b9c85cc49ca17ce25f263c182a097393","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-12-22T23:37:28Z","title_canon_sha256":"21d30b9d98414c5378d41f1a8c058b2ed119fc4c8ee62f348919a27f7e856816"},"schema_version":"1.0","source":{"id":"1112.5491","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.5491","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"arxiv_version","alias_value":"1112.5491v8","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5491","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"pith_short_12","alias_value":"MNAVZBSGYQG3","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MNAVZBSGYQG3BMND","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MNAVZBSG","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:860a30f60eff7b8f260b9ebda30e4b4dd7f828c8592ed243d53adc9503998884","target":"graph","created_at":"2026-05-18T02:47:53Z","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"},"paper":{"abstract_excerpt":"Strong shockwaves generate entropy quickly and locally. The Newton-Hamilton equations of motion, which underly the dynamics, are perfectly time-reversible. How do they generate the irreversible shock entropy? What are the symptoms of this irreversibility? We investigate these questions using Levesque and Verlet's bit-reversible algorithm. In this way we can generate an entirely imaginary past consistent with the irreversibility observed in the present. We use Runge-Kutta integration to analyze the local Lyapunov instability of the forward and backward processes so as to identify those particle","authors_text":"Carol G. Hoover, Wm. G. Hoover","cross_cats":["nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-12-22T23:37:28Z","title":"Time's Arrow for Shockwaves ; Bit-Reversible Lyapunov and \"Covariant\" Vectors ; Symmetry Breaking"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5491","kind":"arxiv","version":8},"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:ce17d3ecb2de36e242f9817148082fe744a5b89b45ec2eb1252d16ac025af5df","target":"record","created_at":"2026-05-18T02:47:53Z","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":"892026f13fb0d894156d135770542af4b9c85cc49ca17ce25f263c182a097393","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-12-22T23:37:28Z","title_canon_sha256":"21d30b9d98414c5378d41f1a8c058b2ed119fc4c8ee62f348919a27f7e856816"},"schema_version":"1.0","source":{"id":"1112.5491","kind":"arxiv","version":8}},"canonical_sha256":"63415c8646c40db0b1a3aa82b86158cd2893c6911c32041f1a5491df360502c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63415c8646c40db0b1a3aa82b86158cd2893c6911c32041f1a5491df360502c8","first_computed_at":"2026-05-18T02:47:53.240530Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:53.240530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Fm+sYMwkssf0gdepnPefOPhCgk49seW8z8NNviJug6pVy4x0azOOLlo8807sPi7U6Bkkcw6ks/ZWQPVuBlKCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:53.241070Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.5491","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce17d3ecb2de36e242f9817148082fe744a5b89b45ec2eb1252d16ac025af5df","sha256:860a30f60eff7b8f260b9ebda30e4b4dd7f828c8592ed243d53adc9503998884"],"state_sha256":"2422401c774e70554a72a1b11c22bee1fb66b27e24d41e4bdf7e6ec26d7e1fe9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1fEuUyWcOq2aPadmyGgo9y0h3nlSPyDkLF95f7ZSeCstT+IMAH5MlN8OTAo0xtTls/kjs7ZOx9LgCz+TlEDSDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T18:05:53.196452Z","bundle_sha256":"b6dd62355abb7599b36462377fab4b487e5722d59d66399a492e19ae99386f2b"}}