{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:UEXI2IGO2N7TX75RBRENWEYPVJ","short_pith_number":"pith:UEXI2IGO","canonical_record":{"source":{"id":"1306.5894","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2013-06-25T09:20:27Z","cross_cats_sorted":[],"title_canon_sha256":"0673a630e44dde02c8a6ab3453bda304bc5356195551df49f38d9bddc96fd421","abstract_canon_sha256":"f0402f31022a010d65c073c053692790b3722c84b6960abaf163a5eed97e83bc"},"schema_version":"1.0"},"canonical_sha256":"a12e8d20ced37f3bffb10c48db130faa59c8d2a7470f27f6100231f79f0ff1ec","source":{"kind":"arxiv","id":"1306.5894","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5894","created_at":"2026-05-18T01:49:08Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5894v1","created_at":"2026-05-18T01:49:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5894","created_at":"2026-05-18T01:49:08Z"},{"alias_kind":"pith_short_12","alias_value":"UEXI2IGO2N7T","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UEXI2IGO2N7TX75R","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UEXI2IGO","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:UEXI2IGO2N7TX75RBRENWEYPVJ","target":"record","payload":{"canonical_record":{"source":{"id":"1306.5894","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2013-06-25T09:20:27Z","cross_cats_sorted":[],"title_canon_sha256":"0673a630e44dde02c8a6ab3453bda304bc5356195551df49f38d9bddc96fd421","abstract_canon_sha256":"f0402f31022a010d65c073c053692790b3722c84b6960abaf163a5eed97e83bc"},"schema_version":"1.0"},"canonical_sha256":"a12e8d20ced37f3bffb10c48db130faa59c8d2a7470f27f6100231f79f0ff1ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:49:08.180603Z","signature_b64":"29pbqYM+dgJWqxt7UzyVU8bQumPPU34bCyvx1/jJCS/4kbfYBzRnYYfzYCD4NJDUhgOryGb27hI1NizMRETFAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a12e8d20ced37f3bffb10c48db130faa59c8d2a7470f27f6100231f79f0ff1ec","last_reissued_at":"2026-05-18T01:49:08.179772Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:49:08.179772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.5894","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":"2026-05-18T01:49:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3WzSpz4bq7HejrDr6ok4Tvk2Tmgc2/xkTlZR2K+H8+vqFmXdA80WQsoU9a9MNh/xFrfrbLPsaWtFMZDbvWxAAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T20:58:10.464515Z"},"content_sha256":"9930f76f9a30b4e5b2ba8bb8376292139c26b96b2d3a86c095ac8458280995d1","schema_version":"1.0","event_id":"sha256:9930f76f9a30b4e5b2ba8bb8376292139c26b96b2d3a86c095ac8458280995d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:UEXI2IGO2N7TX75RBRENWEYPVJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"High-frequency vibrational density of states of a disordered solid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Constantin Tomaras, Walter Schirmacher","submitted_at":"2013-06-25T09:20:27Z","abstract_excerpt":"We investigate the high-frequency behavior of the density of vibrational states in three-dimensional elasticity theory with spatially fluctuating elastic moduli. At frequencies well above the mobility edge, instanton solutions yield an exponentially decaying density of states. The instanton solutions describe excitations, which become localized due to the disorder-induced fluctuations, which lower the sound velocity in a finite region compared to its average value. The exponentially decaying density of states (known in electronic systems as the Lifshitz tail) is governed by the statistics of a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5894","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":""},"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":"2026-05-18T01:49:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2XVEU8D37vLQhOM20yLUDLqibd/+l49Mb7RXC+p+GtSYtuqLRMLwXpQS4k/wUAY80A6Qd8nfj3l8F38BHaZxDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T20:58:10.464893Z"},"content_sha256":"37a804c661ff0055f98110b9cd34a44a81a5710c82556a22dcfd83756f66bd8d","schema_version":"1.0","event_id":"sha256:37a804c661ff0055f98110b9cd34a44a81a5710c82556a22dcfd83756f66bd8d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UEXI2IGO2N7TX75RBRENWEYPVJ/bundle.json","state_url":"https://pith.science/pith/UEXI2IGO2N7TX75RBRENWEYPVJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UEXI2IGO2N7TX75RBRENWEYPVJ/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":"2026-05-19T20:58:10Z","links":{"resolver":"https://pith.science/pith/UEXI2IGO2N7TX75RBRENWEYPVJ","bundle":"https://pith.science/pith/UEXI2IGO2N7TX75RBRENWEYPVJ/bundle.json","state":"https://pith.science/pith/UEXI2IGO2N7TX75RBRENWEYPVJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UEXI2IGO2N7TX75RBRENWEYPVJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UEXI2IGO2N7TX75RBRENWEYPVJ","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":"f0402f31022a010d65c073c053692790b3722c84b6960abaf163a5eed97e83bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2013-06-25T09:20:27Z","title_canon_sha256":"0673a630e44dde02c8a6ab3453bda304bc5356195551df49f38d9bddc96fd421"},"schema_version":"1.0","source":{"id":"1306.5894","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5894","created_at":"2026-05-18T01:49:08Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5894v1","created_at":"2026-05-18T01:49:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5894","created_at":"2026-05-18T01:49:08Z"},{"alias_kind":"pith_short_12","alias_value":"UEXI2IGO2N7T","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UEXI2IGO2N7TX75R","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UEXI2IGO","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:37a804c661ff0055f98110b9cd34a44a81a5710c82556a22dcfd83756f66bd8d","target":"graph","created_at":"2026-05-18T01:49:08Z","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":"We investigate the high-frequency behavior of the density of vibrational states in three-dimensional elasticity theory with spatially fluctuating elastic moduli. At frequencies well above the mobility edge, instanton solutions yield an exponentially decaying density of states. The instanton solutions describe excitations, which become localized due to the disorder-induced fluctuations, which lower the sound velocity in a finite region compared to its average value. The exponentially decaying density of states (known in electronic systems as the Lifshitz tail) is governed by the statistics of a","authors_text":"Constantin Tomaras, Walter Schirmacher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2013-06-25T09:20:27Z","title":"High-frequency vibrational density of states of a disordered solid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5894","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":"sha256:9930f76f9a30b4e5b2ba8bb8376292139c26b96b2d3a86c095ac8458280995d1","target":"record","created_at":"2026-05-18T01:49:08Z","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":"f0402f31022a010d65c073c053692790b3722c84b6960abaf163a5eed97e83bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2013-06-25T09:20:27Z","title_canon_sha256":"0673a630e44dde02c8a6ab3453bda304bc5356195551df49f38d9bddc96fd421"},"schema_version":"1.0","source":{"id":"1306.5894","kind":"arxiv","version":1}},"canonical_sha256":"a12e8d20ced37f3bffb10c48db130faa59c8d2a7470f27f6100231f79f0ff1ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a12e8d20ced37f3bffb10c48db130faa59c8d2a7470f27f6100231f79f0ff1ec","first_computed_at":"2026-05-18T01:49:08.179772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:08.179772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"29pbqYM+dgJWqxt7UzyVU8bQumPPU34bCyvx1/jJCS/4kbfYBzRnYYfzYCD4NJDUhgOryGb27hI1NizMRETFAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:08.180603Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.5894","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9930f76f9a30b4e5b2ba8bb8376292139c26b96b2d3a86c095ac8458280995d1","sha256:37a804c661ff0055f98110b9cd34a44a81a5710c82556a22dcfd83756f66bd8d"],"state_sha256":"e85d57b34500cdc6189595adb4e9b988e8ed256a2b2e9cde9c2e4f9cdbce1f02"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gkYdEl4S5x0WOfZIQzbQVVHcH2jF5iJ/SbeeZKRPasIcW2hrgMNVkLmIUWFrg5+JU4inlPNljiEap5lpVqFABA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T20:58:10.466919Z","bundle_sha256":"1cb2147352841d0fa095eba380418014c29032f4464d0389b4094e2cb582dcdd"}}